Topology studies how a shape or object is connected. In the past few years, there has been an increased interest in the development and use of topological methods for solving various problems in science and engineering. This new line of study is called Computational Topology or Applied Algebraic Topology. Computational topology combines topological results with efficient algorithms to analyze data and solve problems in many fields, including computer graphics and image analysis, neural networks and sensor networks, clustering, robotics, genetics, protein biochemistry, geography, and others. The aim of this course is to give a crash course on topology and geometry with an emphasis on the algorithmic computations for students who are interested in the application side of mathematics.