abstract algebra – What does the notation \$mathbb{Z}_q[X]/(X^n+1)\$ mean and how is multiplication defined there?

I recently encountered the notation which is referred to as ring (in the description of a cryptography scheme, Dilithium, here, page 4):

(…) The key generation algorithm generates a $$k times l$$ matrix $$bf{A}$$ each of whose entries is a polynomial in the ring $$R_q = mathbb{Z}_q/(X^n+1)$$

I am not entirely sure how to read this notation:

• Is this simply the polynomials of maximum degree where all coefficients are in $$Z_q$$?
• How is the multiplication of two polynomials defined in this ring?
• Does the matrix $$bf{A}$$ now consist of $$l$$ polynomials or $$k times l$$ polynomials?