This book highlights the practical benefits of advanced mathematics through real-world applications in various engineering fields, such as sustainable engineering, innovative algorithms, reliability engineering, systems engineering, and soft computing. It covers essential mathematical models for environmental and economic sustainability, cutting-edge algorithms with practical examples, and models in reliability engineering to improve system performance under uncertainty. The systems engineering section explores methods for designing and optimizing complex systems with case studies, while soft computing delves into fuzzy logic, neural networks, and genetic algorithms. Balancing theory with hands-on examples, this book simplifies complex topics and offers innovative solutions to global engineering challenges, making it an accessible guide for those wanting to deepen their understanding of advanced mathematics in engineering.