This manual describes the use of PETSc 2.0 for the numerical solution of partial differential equations and related problems on high-performance computers. The Portable, Extensible Toolkit for Scientific Computation (PETSc) is a suite of data structures and routines that provide the building blocks for the implementation of large-scale application codes on parallel (and serial) computers. PETSc 2.0 uses the MPI standard for all message-passing communication. PETSc includes an expanding suite of parallel linear and nonlinear equation solvers that may be used in application codes written in Fortran, C, and C++. PETSc provides many of the mechanisms needed thin parallel application codes, such as simple parallel matrix and vector assembly routines that allow the overlap of communication and computation. In addition, PETSc includes growing support for distributed arrays. The library is organized hierarchically, enabling users to employ the level of abstraction that is most appropriate for a particular problem. By using techniques of object-oriented programming, PETSc provides enormous flexibility for users. PETSc is a sophisticated set of software tools; as such, for some users it initially has a much steeper learning curve than a simple subroutine library. In particular, for individuals without some computer science background or experience programming in C, Pascal, or C++, it may require a large amount of time to take full advantage of the features that enable efficient software use. However, the power of the PETSc design and the algorithms it incorporates make the efficient implementation of many application codes much simpler than rolling them yourself. For many simple tasks a package such as Matlab is often the best tool; PETSc is not intended for the classes of problems for which effective Matlab code can be written. Since PETSc is still under development, small changes in usage and calling sequences of PETSc routines will continue to occur.