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Shin Nihongo no Kiso: Chapter 2 Grammar

日本語 English Notes
これは A です。 This is an A. Japanese doesn't have articles ("a", "an" or "the"). That doesn't mean that the language can't express subtleties that English expresses using articles. In this particular case, if you wanted to say "This is the A", you might say 「これが A です。」 or 「これが れいの A です。」 (れいの = the one we were talking about). Note the change of particle, and remember that when you're making a simple statement about the nature or identity of something or someone, use 「〜は〜です。」.
A は B の C です。 A is B's C. の is the possessive marker. Japanese has no possessive pronouns or adjectives like English "my" or "mine", but just uses regular pronouns (e.g. わたし I) with の (e.g. わたしの my).
この A は B の です。 This A is B's. Adjectives and pronominal adjectives (like この this) go in front of their nouns, just as in English. And as in English, a possessive doesn't need to have a noun after it (わたしの mine).