In this first part of the MA010 course the students will learn many basic graph terms and concepts, with the focus on traditional areas of application of graphs in informatics and computing. Some topics are thus overlapping with the first-year IB000 (and other discrete math) course and with subsequent bachelor courses on algorithms. This course, though, puts more stress on the mathematical side of the presented algorithmic applications and on understanding of why the applications work. Some less-known and more advanced extensions are briefly surveyed, too.