The course will provide students with basic concepts of the theory of graphs and with some algorithms based on that theory. After the basic definitions, the classic problems will be discussed including the Euler path and Hamilton cycle of a graph, vertex colouring, planar graphs etc. The next concept to be investigated will be trees and tree-based algorithms. Attention will also be paid to the problem of finding the shortest path in a graph. Students will also learn about bipartite graphs and matching problems. Oriented graphs will be introduced to build networks and flows in them and deal with algorithms used to find a critical path. The course will be oriented towards applications of graphs that can be found in many areas of practical life. Emphasis will be placed on applications in computer science, optimization and theory of control and in operation research.