Exchangeability and related topics by PAR David J. Aldous. In 1970, a probabilist would have said that the only known result about exchangeability was de Finetti's theorem. This text aims to change that by presenting various post-1970 results on exchangeability in Parts II-IV. The topics are chosen based on the author's interests, avoiding areas with existing surveys. Most of the text is accessible to students who have taken a standard first-year graduate course in measure-theoretic probability, though some sections require knowledge of weak convergence. In Bayesian terms, de Finetti's theorem states that an infinite-dimensional exchangeable sequence (Z_i) can be obtained by first selecting a distribution θ from a prior, and then taking (Z_i) as i.i.d. with distribution θ. In probability theory terms, the theorem states that we can associate a random distribution α(ω,·) with (Z_i), such that, conditional on α=θ, the variables (Z_i) are i.i.d. with distribution θ. This formulation is central to the ideas surrounding de Finetti's theorem, which is covered in Part I. No prior knowledge of exchangeability is assumed, though readers who find the proofs too concise should consult Chow and Teicher (1978), Section 7.3. Part II contains results complementary to de Finetti's theorem. Dacunha-Castelle's "spreading-invariance" property and Kallenberg's stopping time property give conditions on an infinite sequence equivalent to exchangeability. Kingman's "paintbox" description of exchangeable random partitions leads to Cauchy's formula for the distribution of partitions.Exchangeability and related topics by PAR David J. Aldous. In 1970, a probabilist would have said that the only known result about exchangeability was de Finetti's theorem. This text aims to change that by presenting various post-1970 results on exchangeability in Parts II-IV. The topics are chosen based on the author's interests, avoiding areas with existing surveys. Most of the text is accessible to students who have taken a standard first-year graduate course in measure-theoretic probability, though some sections require knowledge of weak convergence. In Bayesian terms, de Finetti's theorem states that an infinite-dimensional exchangeable sequence (Z_i) can be obtained by first selecting a distribution θ from a prior, and then taking (Z_i) as i.i.d. with distribution θ. In probability theory terms, the theorem states that we can associate a random distribution α(ω,·) with (Z_i), such that, conditional on α=θ, the variables (Z_i) are i.i.d. with distribution θ. This formulation is central to the ideas surrounding de Finetti's theorem, which is covered in Part I. No prior knowledge of exchangeability is assumed, though readers who find the proofs too concise should consult Chow and Teicher (1978), Section 7.3. Part II contains results complementary to de Finetti's theorem. Dacunha-Castelle's "spreading-invariance" property and Kallenberg's stopping time property give conditions on an infinite sequence equivalent to exchangeability. Kingman's "paintbox" description of exchangeable random partitions leads to Cauchy's formula for the distribution of partitions.