The book discusses the geometry of matrices over some rings and their applications in algebra and geometry. The first part of the book is concerned with rings and modules, matrices over a ring, affine geometry and projective geometry over a ring, affine geometry and projective geometry over a bezout domain. later in the book, more advanced topics, such as the geometry of rectangular matrices over a bezout domain or a semisimple ring, the geometry of hermitian matrices or skew-hermitian matrices over a division ring, the geometry of symmetric matrices over a principal ideal domain and the geometry of block triangular matrices over a division ring are discussed in detail.