This book provides an easy-to-read introduction to quantum computing, as well the classical simulation of quantum circuits with common types of error effects. The authors showcase the enormous potential that can be unleashed when doing these simulations using decision diagrams-a data-structure common in the design automation community, often used in quantum computing design tasks. The algorithms and methods described can outperform previously proposed solutions in some cases, providing a complementary solution to established approaches. Finally, the necessity of noise-aware classical quantum circuit simulation is demonstrated through a practical use-case: the evaluation of quantum error correcting codes.