The book "Numerical Partial Differential Equations" from Springer offers a comprehensive introduction to numerical methods for solving partial differential equations, with a particular focus on finite difference methods. It is aimed at students of applied mathematics and engineering who are at the beginning of their academic careers. The text imparts both theoretical knowledge and practical experience in numerical experimentation. Readers are encouraged to actively use technology to better understand and apply the concepts. Graphical representations are employed for illustration and analysis, and algebraic manipulators are used where appropriate. This book is the second volume of a two-volume series and assumes a foundational knowledge of partial differential equations as well as programming skills.