Proto-Indo-European is a language hypothesized to be the ancestor of most of the languages of Europe and quite a few languages of Asia. These descendants are called Indo-European languages (or Indogermanic or Aryan in some sources).

PIE itself would have been spoken several thousand years ago--at least two thousand years before the invention of writing--so we can have no written records of it. What we know of its words has been reconstructed using the comparative method, which means searching for correspondences in the daughter languages and hypothesizing regular changes to account for them. For example, we can say that English "brother" and Greek "phrater" are related, as English b and Greek ph regularly correspond to PIE *bh, and th and t to IE *t. (The full root is *bhreH2-ter-.)

Phonology

PIE has usually been reconstructed as having five series of stops:

      Labial: p  b  bh
      Dental: t  d  dh
     Palatal: k' g' gh'
       Velar: k  g  gh
  Labiovelar: kw gw ghw

The first column are voiceless, the second voiced, the third voiced aspirated, although these were most likely not their actual values. For example, PIE *b is rare, and it's not common in existing languages to have voiced aspirates without also having voiceless aspirates. The Glottalic Hypothesis reinterprets the second column as "glottalized" voiceless (ejectives) and the third column as voiced. This fits the reconstruction better, as it is common for languages with ejectives to not have a labial ejective. An alternate theory is that *b had already merged with *w in pre-PIE times, and IIRC this hypothesis is supported by several *w-initial homophonous roots (but I'm not sure of this offhand).

The generic root structure of Proto-Indo-European was CVC, where the vowel is usually *e, but can ablaut to *o or to zero (nothing). A regular PIE root cannot have two consonants from the second column, and it cannot have both one from the first column and one from the third column.

The only fricative in PIE is *s. There are two nasals, *m and *n; two liquids, *r and *l; and two glides, *y and *w. The laryngeals may have been fricatives, though, and are occasionally so reconstructed.

PIE had very few vowels. For certain, there is *e. There are also *i and *u, which are syllabic versions of *y and *w. *o interchanges with *e by ablaut. *a and *o also can appear as *e is colored by a laryngeal. The laryngeals are sounds that disappeared from PIE and only appear historically in Anatolian languages like Hittite. Their effect was to "color" the preceding or following *e to another vowel, and to lengthen a preceding vowel. *H1 was "uncolored", *H2 was "a-colored", and *H3 was "o-colored".

If that's difficult, an example: later PIE *do:- would represent an earlier PIE *deH3- and a later PIE *an- would probably represent earlier PIE *H2an-.

Besides laryngeals, the palatals were also lost in many languages. Rather, the palatals in many languages (the "centum" languages) merged with the velars. In other languages (the "satem" languages) the palatals remained distinct from the velars, usually becoming sibilants. The terms centum and satem come from the Latin and Sanskrit words for "a hundred" and are examples of the division. An alternate theory is that the "plain" velar *k *g *gh series didn't exist; the number of *k/*g/*gh-containing roots is thought to be overestimated because this is the "default" bin they are put into when comparative evidence can't place them firmly in the conventional palatal or labiovelar series. Under this theory satem languages shifted the conventional palatals to sibilants, and the centum ones kept them as velar stops.

Morphology

Nouns

PIE nouns decline for case and number. There are different endings depending on the ending of the root/stem. The cases generally reconstructed are nominative, vocative, accusative, instrumental, dative, genitive, ablative, and locative.

The following table is appropriated from New Comparative Grammar of Greek and Latin by Andrew Sihler. An equals sign follows a syllabic resonant, and 0 indicates an absence of an ending. (neut) indicates the nominative and accusative of neuter nouns, which are identical. eH2-stems are more commonly recognized as a:-stems.

Singular
     Cons-stem  o-stem  eH2-stem    i-stem  u-stem
Nom  -s/-0      -o-s    -eH2-0      -i-s    -u-s
Voc  -0         -e-0    -eH2-0      -ey-0   -ew-0
Acc  -m=        -o-m    -eH2-m      -i-m    -u-m
(neut) -0       -o-m      N/A       -i-0    -u-0
Ins  -bhi,      -o-H1,  -eH2-bhi,   -i-bhi  -u-bhi
     -mi,       -e-H1   -eH2-eH1 ?  -i-H1   -u-H1
     -(e)H1
Dat  -ey        -o:y    -eH2-ey     -ey-ey  -ew-ey
Gen  -s,        -i:,    -eH2-es,    -oy-s   -ow-s
     -os,       -osyo   -eH2-os
     -e s
Abl  = Gen      -o:t,   = Gen       = Gen   = Gen
                -a:t
Loc  -i/-0      -o-y    -eH2-i      -e:y-0  -e:w-0
                -e-y

Plural
        Cons-stem  o-stem   eH2-stem    i-stem    u-stem
Nom/Voc -es        -o:s     -eH2-es     -ey-es    -ew-es
(pron.)            -oy
Acc     -m=s       -o-ms    -eH2-ms     -i-ms     -u-ms
neut.   -H2        -eH2      N/A        -i-H2     -u-H2
Ins     -bhis,     -o:ys,   -eH2-bhis,  -i-bhis,  -u-bhis,
        -mis,      -o-mis,? -eH2-mis,   -i-mis,   -u-mis,
        -mi:s      -o-mi:s? -eH2-mi:s,  -i-mi:s,  -u-mi:s
Gen     -om ?      -o:m     -eH2-om     -y-om     -w-om
(pron.)            -oyso:m  -eH2so:m
Dat/Abl -bhos,     -o-bhos, -eH2-bhos,  -i-bhos,  -u-bhos,
        -mos,      -o-mos   -eH2-mos,   -i-mos    -u-mos
Loc     -su        (-o-su)? -eH2-su     -i-su     -u-su
(pron.)            -oysu

There was a dual, which is weak even in PIE and doesn't survive in many IE languages, and reconstructing the endings appears to be problematic, the most secure appears to be the m./f. dual nom./acc./voc., being *-H1 (although it might have been *-H1e, or *-e, or even *-H3 apparently).

Ablaut also appears, especially in root nouns. The details of this are complicated and will appear later...

Verbs

...verbs are also complicated. I will put up more later, but till then here are the personal endings for active verbs as reconstructed (source same as above)

Secondary Endings
      sg      du     pl
1st  -m/-m=  -we(:) -me(:)
2nd  -s      -tom   -te
3rd  -t      -ta:m  -nt/-n=t/-r=/-e:r

Primary Endings
      sg        du     pl
1st  -oH2/-mi  -wos   -mos
2nd  -si       -tH1es -te
3rd  -ti/-i    -tes   -nti/-n=ti

Descendants

PIE gave birth to the following families:

Albanian
Anatolian
Extinct languages such as Hittite and Luvian.
Armenian
Balto-Slavic
Languages of Eastern Europe, such as Russian, Lithuanian, Latvian, Polish, and Czech. Lithuanian became famous in PIE for how well it preserved the ancient word endings.
Celtic
Languages of Western Europe, such as Welsh, Irish Gaelic, and Scots Gaelic. Two major branches of Celtic are Goidelic and Brittonic, called "q-Celtic" and "p-Celtic" respectively, based on their separate reflexes of PIE *kw.
Germanic
Languages of Northern and Western Europe, such as German, Afrikaans, English, Swedish, and Yiddish.
Hellenic
Basically just Greek, which has history all the way back to Linear B...
Illyrian
Italic
Latin and all its descendants (Spanish, Romanian, French...) as well as extinct languages like Oscan and Faliscan.
Indo-Iranian
Also "Indo-Aryan". Most of the Asian PIE languages: Avestan, Persian, Sanskrit and its descendants (Hindi, Bengali, Romany...)
Messapic
Phrygian
According to myth the forbidden experiment once determined this was the original language of mankind...
Thracian
Tocharian
Once spoken in what is now a part of China, its languages are imaginatively titled Tocharian A and Tocharian B.
Venetic

The Italic and Celtic families are generally thought to be closer to each other (or even Italo-Celtic), and similarly with Balto-Slavic and Germanic.

There are theories that Proto-Indo-European is related to other language families. Some proposals, like Nostratic, try to continue the comparative method, but it is not universally agreed that the comparative method can give accurate results with the span of time involved. Others, such as Greenberg's Eurasiatic, use different methods that are not as widely approved.


Whew, glad that's over...