1. Participles.
Active participles may be called just verbal adjectives (like in Gaelic), for they are declined and act as qualitative adjectives of the 1st and 2nd classes. The only exception is the endings in nominative singular and plural. The original suffix for present active participles was -nt- with the corresponding thematic vowel connecting the root with the suffix. The suffix of past active participles is -us-, and it was the same in Proto-Indo-European. Here are the forms of active participles, given only in nominative, but can always see how qualitative adjectives are declined, and decline a participle the same way. Here are the forms, and note that the participles reflect the verbs of corresponding conjugations:

Present active participles:

Past active participles:

There are also active participles of the Future tense. They can be formed by the present tense stem + the future tense suffix -s- + the endings of the present participles seen above (e.g. dirbsanti žmona - a woman that will work). The same order is valid with active participles of the Past Habitual tense: present stem + suffix -dav- + endings of past simple participles (e.g. dirbdavusi žmona - the woman that used to work)

The usage of active participles in the Lithuanian sentence has several cases:
    a) they can behave as an attribute (Tekantis vanduo búna švarus - Flowing water can be clear [a proverb])
    b) they can act as an adverbail modifier (Gri,že,s pavalgiau - Having come, I had a meal)
    c) past active participles can be a part of the nominal predicate, and it looks like the English or French perfect (Aš esu skaite, ta, knyga, - I have read this book)

Passive participles are declined simply like 1st class adjectives; they have a short suffix and simple adjective endings following it. Passive participles can be used as attributes:
    Važiavau neseniai nutiestu keliu - I was driving along the road laid recently
or as a part of a nominal predicate:
    Aš buvau kvečiamas i, pose.di, - I was invited to the meeting
or - in neuter gender - in an impersonal construction:
    Visur nutarta , kad rúkyti žalinga - It is written everywhere that smoking is prohibited

The nominative forms are as follows:
a) present
        the 3rd person present + -mas (masc. sg.), -ma (fem., neut. sg.), -mi (masc. pl.), -mos (fem., neut. pl.)
        Aš esu kvečiamas - I am invited

b) past
        the infinitive stem + -tas, -ta, -ti, -tos
        Atvyko músu, seniai lauktas svečias - Our long awaited guest has come

c) future (expresses necessity or obligation)
        the infinitive stem + -tinas, -tina, etc.
        Jis yra ateitinas vyras - He is a man who is expected to come

Semi-participles and verbal adverbs are considered as just participles; this can go formally with semi-participles, but the main difference between a participle and a verbal adverb is that the second cannot be declined, it has only one form, though the suffixes of active participles and verbal adverbs are the same.

Semi-participles are formed by adding the -damas suffix to the infinitive stem and are declined as 1st class adjectives. They are syntaxically used to mark the action simultaneous with the predicate:
    Gri,ždamas iš instituto jis užeis i, biblioteka, - While returning from the institute, he will drop into the library

Verbal nouns mark the action of the object in the sentence, or can be used in impersonal sentences. For more understanding see for yourself:
a) present
        the present stem + -ant (in 1st and 3rd conjugation verbs), -int (in the 2nd conjugation verbs)
        Saulei (note dative case) tekant, čiulbe.jo paukščiai - The sun was rising, the birds were singing (lit. "The sun rising, the birds singing)
        Man skaitant , kažkas pasibelde. i, duris - When (I was) reading, someone knocked at the door
        Stojant i, instituta, , reike.jo laikyti egzaminus - When entering the institute, I had to take exams

b) past simple
        the past simple stem + -us (1-2 conjugation), -ius (3rd conjugation)
        Baigus darba, , galima pailse.ti - Having finished the work, one can take a rest
        Ji e.jo namo palijus - She went home after the rain
 
c) past habitual
        the infinitive stem + -davus
 
d) future
        the present stem + -siant

The rest of verbal substantives in Lithuanian include infinitives and the supine. The Proto-Indo-European language had no infinitive, it used only some verbal nouns to express the indefinite form of the predicate. That is why the infinitives in different Indo-European languages were derived from different verbal noun forms. Latin had 6 infinitives, and English uses 4 or even 8 varieties nowadays. Russian has only one, and Lithuanian - two infinitives.

The first one has a -ti ending and was widely used in examples of the present article. It has simple infinitive functions: dirbti, nore.ti, laikyti are used the same way as "to work, to want, to hold". The second infinitive has a -te ending and is seldom heard in modern colloquial speech - just in some emphasis constructions: be.gte be.ga - "he is running and running" (lit. "he is runnning by run).

The supine has -tu, derived from -tum after the infinitive stem. It means just another variety of infinitive used only after the verbs of movement:
    Iše.jo pavaikščioti - went for a walk

That's all for the Lithuanian verb and its derivatives, I think. Don't you?
 
 
     § 10. The Lithuanian Preposition.
 
The Proto-Indo-European language did not have any prepositions, they were just appearing from adverbs and adjectives, becoming the auxiliary part of speech. That is why all branches already used prepositions or postpositions, using them with nouns of this or that case.

Lithuanian places prepositions before genitive, accusative and instrumental. When it had the ablative case (in Common Balto-Slavic epoch) some prepositions also used it, and now they joined genitive nouns. Here is the table:
 
1. With genitive:
ant - on, upon (where?)
be - without
de.l - due to, because of
iki - until, till
iš - from, since, out of (former ablative)
nuo - since (time), from (former ablative)
prie - near, next to, towards
šalia - near, next to, nearby
tarp - between, among
už - behind
virš - above
po - after, in (some time)
link - towards (a postposition)

2. With accusative:
apie - about, near, approximately
aplink - around
i, - in (where? and whither?)
pas - at somebody's, to, towards
per - through, during (per vasara, - for the summer, per gatve, - along the street)
pro - through, past (pro langa, - through the window, pro mane - past me)
prieš - before, in front of, against, ago
po - along, through (vaikščioti po soda, - to walk all through the garden, duoti visiems po obuoli, - to give everyone an apple)
už - instead of, for (pirkti už  lita, - to buy for a litas)

3. With instrumental:
su - with
po - under
 
 
     § 11. The Lithuanian Conjunction, Particle and Interjection.
 
1. Coordinative conjunctions.
ir - and
o - and, but (co-incides with Russian a)
bet - but
tačiau - however
ar, arba - or, else

2. Subordinative conjunctions.
nes - as, because (tearing the main and the clause)
kadangi - as, because of (at the beginning of the sentence)
tode.l kad - because
jei - if
kad - that
kaip - than (with a verb)
negu - than (with a noun)
kuris - which (see Pronouns)
kol - until
juo... juo - the (more)... the (better)

3. Particles.
ar - an interrogative particle
ne - a negative particle (not with verbs, see Verbs)
štai - here (štai mano motina - this (here) is my mother)
juk - emphatic particle (corresponding to Russian ved')
gi - doesn't have a corresponding word in English, equals Russian zhe or Latin autem

4. Interjections.
taip - yes (lit. "so")
ne - no
na - well
 
 
     § 12. The Lithuanian Syntax.
 
The Lithuanian syntax is purely Indo-European, and this is very pleasant: for me personally it is always nice to see the subject at the beginning and the predicate after the subject. However, there are some languages where other features were developed: Latin often has the predicate at the end, German moves the negatives to the final position. Lithuanian is easier here: the word order, though frequently free, has actually the fixed form:    subject - predicate - objects - adverbial modifiers. For example:
    Motina , paklause. dukteri, nupirkti duonos parduotuve.je. - Mother asked daughter to buy some bread in the shop.

And the attribute is placed before the noun: mano sesuo, Juozapo žmona, gramatine.s sistemos raida - my sister, Joseph's wife, the grammar system development.

Now some constructions important not only for better understanding of Lithuanian grammar, but also for colloquial language.

1. The obligation.
    subject in dative case + reikia (needs) + infinitive:
        Man reikia eiti i, dirba, - I need to (have to, should) go to work
 
    the form of the verb ture.ti (to have) + infinitive:
        Ji turi mums pakviesti - She should invite us

2. The possibility.
    subject in dative case + galima (may) + infinitive:
        Mums galima nusipirkti šita, laikrašti, - We may (can) buy this newspaper
 
    the form of the verb gale.ti (to may) + infinitive:
        Galiu nedaug pavaikščioti - I can walk a little

3. The indirect speech.
    Jis sake. man , kad šiandien ateis pas mane - He told me, that today he would come to me
    (note: no sequence of tenses in Lithuanian)

    Jis klause. man , ar aš eisiu i, teatra, - He asked me, if I would go to the theater.
    (note the interrogative particle ar in interrogative clauses)

    Jis klause. man , kur aš gyvenu - He asked me, where I lived

    Jis praše. mane kad aš nupirkčiau jam šita, laikrodi, - He asked me to buy him this watch.
    (note the subjunctive mood after the conjunction kad in such clauses, also seen in Aš einu ten kad nupirkčiau duonos - I go there to buy some bread)

Laima.    Rimas, wasn't there evening newspaper yet?
Rimas.    It was already. And what do you want to learn?
Laima.    To watch the tomorrow weather forecast. You know, we were preparing to go skiing.
Rimas.    Here's the newspaper, read aloud.
Laima.    In Vilnius tonight the temperature was 23 degrees below zero, and in the day at 13 o'clock 21 degrees below zero.
              Tomorrow in Vilnius still will be cold weather. The temperature at night 15-17, in the day 12-15 degrees below zero.
              Will be snowing a little. The wind will blow from the west.
Rimas.    So what, it's not that cold, we almost can ski.
Laima.    Also in the morning we will listen to the report about the weather. Then we will decide whether we will go or not
              skiing.

Glossary:
Rimai - vocative case of Rimas, used when addressing
ar - an interrogative particle (see)
dar - yet, still
nebuvo - was not
vakarinio - genitive case of vakarinis (evening, adj.); see Relative Adjectives
laikraščio - genitive of laikraštis (a newspaper)
jau - already
yra - is, are (3rd person)
o - and, but
ka, - accusative of kas (what, who)
tu - you (singular)
nori - want, wants (2nd and 3rd person)
sužinoti - to learn (a prefix su- to the verb "to know" meaning "to have it known")
pažiúre.ti - to have a look, to look, to watch
oro - genitive of oras (weather)
prognoze.s - nominative plural of prognoze. (a forecast)
rytdienai - dative of rytdienas (tomorrow's day)
juk - the emphatic particles (see)
mes - we
ruošiame.s - past simple in the 1st person plural of the verb ruoštis (to prepare oneself)
eiti - to go
slidine.ti - to ski
tai - here, here it is
paskaityk - imperative of the 2nd person singular of the verb skaityti (to read)
balsu - loudly, aloud (neuter adjective)
šiandien - today
Vilniuje - lovcative case of Vilnius
nakti, - at night (the adverb from the noun)
laipsniai - plural of laipsnis (degree)
šalčio - genitive of šaltis (frost, coldness)
diena, - in the day
valanda, - o'clock (accusative)
rytoj - tomorrow
bus - will be
šalti - plural masculine of šaltas (cold)
orai - weather (used here in plural)
laipsniu, - genitive plural of laipsnis (after the numerals more than 10)
truputi, - a little
snigs - 3rd person future of snigti (to snow)
ve.jas - wind
pús - 3rd person future of pústi (to blow)
iš - from (with genitive)
vakaru, - genitive plural of vakaras (evening; west)
na - well (interjection)
ka, - what (accusative)
gi - particle
taip - so
ir - and
beveik - almost
galima - may, can (impersonal)
ryte - in the morning (locative of rytas)
paklausisime - 1st peson plural future of paklausyti (to listen to)
pranešimo - genitive of "report"
apie - abot (with accusative)
tada - then
nuspre,sime - 1st person plural future of nuspre,sti (to decide)
eisime - 1st person plural future of eiti (to go)
neisime - negative of eisime