Every computer scientist and every professional programmer should know about basic algorithm toolbox: structures that allow efficient organization and retrieval of data, frequently used algorithms, and basic techniques for modeling, understanding and solving algorithmic problems. The algorithm is presented in a modern way, with explicitly formulated invariants, and comment on the latest trends such as algorithm engineering, memory hierarchy, algorithms and algorithm library certification. The author uses pictures, words and high-level pseudocode to explain the algorithm, and then they present more detailed implementation efficiently by using a real programming language like C + + and Java. The author has extensive experience teaching these subjects for students and graduates, and they offer a clear presentation, with examples, pictures, informal explanations, exercises, and some relationship to the real world. Most chapters have the same basic structure: the motivation for this problem, comment on the most important applications, and then simple solutions presented as informally as possible and formally required.