These lectures concentrate on fundamentals of the modern theory of linear elliptic and parabolic equations in Hölder spaces. Krylov shows that this theoryincluding some issues of the theory of nonlinear equationsis based on some general and extremely powerful ideas and some simple computations. The main object of study is the first boundaryvalue problems for elliptic and parabolic equations, with some guidelines concerning other boundaryvalue problems such as the Neumann or oblique derivative problems or problems involving higherorder elliptic operators acting on the boundary. Numerical approximations are also discussed. This book, with nearly 200 exercises, will provide a good understanding of what kinds of results are available and what kinds of techniques are used to obtain them. Readership Graduate students and researchers in mathematics, physics, and engineering interested in the theory of partial differential equations. Reviews "Short but not condensed, well organized and gives a stimulating presentation of basic aspects of the theory of elliptic and parabolic equations in Hölder spaces ... an interesting addition for students and instructors."  Zentralblatt MATH "The author has fully achieved his goal ... and has written an impressive book that presents nice material in an interesting way ... this book can be recommended as a thorough, modern and sufficiently broad introduction to partial differential equations of elliptic and parabolic types for graduate students and instructors (and also for individual study) in mathematics, physics, and (possibly) engineering."  Mathematical Reviews Table of Contents  Elliptic equations with constant coefficients in \(\mathbb R^d\)
 Laplace's equation
 Solvability of elliptic equations with constant coefficients in the Hölder spaces
 Elliptic equations with variable coefficients in \(\mathbb R^d\)
 Secondorder elliptic equations in half spaces
 Secondorder elliptic equations in smooth domains
 Elliptic equations in nonsmooth domains
 Parabolic equations in the whole space
 Boundaryvalue problems for parabolic equations in half spaces
 Parabolic equations in domains
 Bibliography
 Index
