Albanian is a direct descendant of a south-west group of Illyrian dialects. However, there have been other hypotheses proposed, among which the following merit to be mentioned.

A. The Pelasgian hypothesis.
Albanian is the continuation of the language of an ancient people called Pelasgians, a hypothesis rather diffused in the 19th century. J.G. von HAHN (1854) formulated in a strict manner the hypothesis that the Albanians are direct descendants of the Illyrians, Macedonians, and Epirotes, and that in the remotest times they formed a united race together with the Latins and the Hellenes called Pelasgians, with their language, the Pelasgian. A. SCHLEICHER gave full authority to this theory of Pelasgian origin with his family tree of languages. Today this is considered a groundless idea.
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B. The Thracian (Dacian) hypothesis.
Albanian is the continuation of the
Thracian language. This thesis, implying an Albanian-Rumanian symbiosis, is supported by students of Rumanian: H. HIRT, K. PAUL, G. WEIGAND, H. BARIC, I. POPOVIC, and I. I. RUSSU. Only scant remains of Thracian exist, but HIRT saw Albanians as descendants of the Thracians. This means that in the early Middle Ages the Albanians moved westward from the central part of the Balkans, but there are no historical records of such a massive
migration. To BARIC Albanian is an Illyricized Thracian dialect.
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C. The Illyrian-Thracian hypothesis. Albanian is derived from a mixture of Illyrian and Thracian. N. JOKL supported the idea of an intermediate position between Illyrian and Thracian. However, Thracian is not better known than Illyrian, and it is difficult to distinguish their specific elements, or to trace a dividing line between Illyrian and Thracian. For JOKL the Albanians are probably the descendants of the Illyrian tribe of Dardanians, living in the interior of the Balkan peninsula, who migrated westward some time in the late Roman period.
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D. The Daco-Moesian hypothesis is sustained by the Bulgarian academician V. GEORGIEV.
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E. The independent hypothesis.
H. KRAHE affirms that Albanian presents an
independent Indo-European language. The vast work of Prof. E. ÇABEJ on Albanian
etymology (1976), an unrivaled synthesis of everything known in this field, refers to remote periods of Albanian as an Indo-European language, without considering the Illyrian language. Following a strict method, the Albanian etymologies would go back to Illyrian forms, which in turn would be traced back to Indo-European roots, like the Italian etymologies going back to Latin forms. E. HAMP (1972) states: "Albanian shows no obvious close affinity to any other Indo-European language;It is plainly the sole modern
survivor of its own subgroup".
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Along with the basic Albanian vowels: a e i o u y, and ë, there are short and long versions that brings the total to 14 vowels. Then, with Gheg there are nasalized vowels: â, ê, î, ô, û, and ŷ so that brings the vowels to 20. Then each nasalized vowel can also be short or long so now we get 26 vowels. Some dialects have a few more front vowels which we could write as é and ö. So 28 vowels. Then Albanian has a few diphthongs: aj ej ij oj uj yj, and ëj; au, eu, iu. There can short and long variations.

Albanian consonants, a ton of those: p/b t/d q/gj k/g ; c/x ç/xh ; f/v th/dh s/z sh/sh h ; l/ll/ r/rr m n/nj j Also we could add these clusters: mb mp nd ng ngj nk nx. Some dialects have the glottal stop, and velarized forms for m, n, and a pure velar ng. I imagine a few dialects have even a few more consonant sounds. So that could bring up the total to around 40 or so. So all in all Albanian as a whole has around 100 sounds or so. Since most Albanians can speak one or more dialects of Albanian, I wouldn't be surprised if an Albanian has around 100 phonemes in the head!