The copula(s) da/desu - verb or not?

Hi everybody!
I am relatively new to Japanese, although I consider myself an amatuer linguist. What a wonderful language - I am thoroughly enjoying my journey through this beautiful language.
I am diving into verbs and have a question regarding the infinitive/dictionary form of da/desu. Is da, in fact, the infinitive/dictionary form of the copula? If so, I thought that all Japanese verbs ended in a syllable that ended in 'u'? Is this copula an exception or am I missing something? Are da/desu technically not verbial forms? If so, why are they conjugated as such?
Thank you in advance for your assistance!
Charusu Ridu
^_^

だ/です is unlike any other grammatical mechanism in other languages that I know of and even within Japanese they work differently than other verbs. They invoke so many exceptions, that I keep them distinct from other verbs in my mind.

Special verb(s).

だ/です belongs to 助動詞 in 国文法(the traditional/pedagogic Japanese grammar). Although the definition of 助動詞 is different from the one of the auxiliary verb in general linguistics.