This book offers a comprehensive discussion of the Bayesian inference framework and demonstrates why this probabilistic approach is ideal for tackling the various modelling problems within quantitative finance. It demonstrates how advanced Bayesian machine learning techniques can be applied within financial engineering, investment portfolio management, insurance, municipal finance management as well as banking. The book covers a broad range of modelling approaches, including Bayesian neural networks, Gaussian processes and Markov Chain Monte Carlo methods. It also discusses the utility of Bayesian inference in quantitative finance and discusses future research goals in the applications of Bayesian machine learning in quantitative finance. Chapters are rooted in the theory of quantitative finance and machine learning while also outlining a range of practical considerations for implementing Bayesian techniques into real-world quantitative finance problems. This book is ideal for graduate researchers and practitioners at the intersection of machine learning and quantitative finance, as well as those working in computational statistics and computer science more broadly.