Lexemes are abstract units in the mental lexicon. (not flected).
Stems are the basis for inflected words (pretty much identical with lexemes)
Roots are he smallest units of the word (that are not divisible).
Bases are the morphological basis for the construction of complex words/word forms
But often they are identical, depending on the word. Can someone illustrate the difference with examples (i don't care about the language) or should i just learn it as it is and be happy with it?