"Algorithms in Real Algebraic Geometry" is a comprehensive textbook that addresses the algorithmic challenges of real algebraic geometry. It covers central topics such as counting real roots, decision-making regarding the existence of solutions for systems of polynomial equations and inequalities, as well as the search for global maxima. These concepts are significant in many scientific and engineering fields. The book provides a coherent and rich knowledge base that is of interest to both mathematicians and researchers in computer science and engineering. It is designed to be accessible to graduate students and, in parts, to undergraduate students as well. The second edition includes current results on topics such as the discriminants of symmetric matrices and global optimization.