The collection corresponds to the combined course of analytic geometry and linear algebra. A large number of problems are given in the following sections: systems of linear equations, matrices and determinants, curves and second-order surfaces, plane transformations, linear transformations of linear, Euclidean and unitary spaces, functions on linear space, affine and point Euclidean spaces, tensors. There are theoretical introductions to all sections. In addition to tasks that contribute to the assimilation of basic concepts, a series of typical tasks with answers are given. Some typical and more complex tasks are equipped with complete solutions. All compilers of the problem book have experience in teaching mathematics at MIPT, and this experience is reflected in the content of the collection.