This advanced course explores the principles and applications of neural networks and numerical methods, with a focus on their relevance to neuroscience and biological systems. Students will delve into various neural network architectures, training algorithms, and their biological inspirations, while also learning essential numerical methods for solving complex problems in neuroscience. The course covers advanced concepts of machine learning, deep learning, and their applications in analyzing neurological data, modeling neural systems, and solving biological problems. Emphasis will be placed on understanding the parallels between artificial neural networks and biological neural systems, as well as the numerical techniques used to simulate and analyze these systems.