The Use of Ultraproducts in Commutative Algebra Ultraproducts and o’ Theorem Flatness Uniform Bounds Tight Closure in Positive Characteristic Tight Closure in Characteristic Zero. Affine Case Tight Closure in Characteristic Zero. Local Case Cataproducts Protoproducts Asymptotic Homological Conjectures in Mixed Characteristic In spite of some recent applications of ultraproducts in algebra they remain largely unknown to commutative algebraists in part because they do not preserve basic properties such as Noetherianity. This work wants to make a strong case against these prejudices. More precisely it studies ultraproducts of Noetherian local rings from a purely algebraic perspective as well as how they can be used to transfer results between the positive and zero characteristics to derive uniform bounds to define tight closure in characteristic zero and to prove asymptotic versions of homological conjectures in mixed characteristic. Some of these results are obtained using variants called chromatic products which are often even Noetherian. This book neither assuming nor using any logical formalism is intended for algebraists and geometers in the hope of popularizing ultraproducts and their applications in algebra