Explore time series modeling and state space models in this comprehensive lecture by Professor Chris Williams from the University of Edinburgh, presented at the Alan Turing Institute. Delve into AR, MA, and ARMA models, learning about their structures and parameter estimation techniques. Gain insights into Hidden Markov Models, including their definitions, inference methods, and learning algorithms. Discover the intricacies of Linear-Gaussian HMMs, with a focus on Kalman filtering. Conclude by examining advanced topics such as elaborate state-space models and recurrent neural networks. This 1 hour and 35-minute presentation offers a thorough introduction to key concepts in time series analysis and state space modeling for data science enthusiasts and professionals.