These lecture notes are designed to accompany an imaginary, virtual, undergraduate, one or two semester course on fundamentals of Parallel Computing as well as to serve as background and reference for graduate courses on High-Performance Computing, parallel algorithms and shared-memory multiprocessor programming. They introduce theoretical concepts and tools for expressing, analyzing and judging parallel algorithms and, in detail, cover the two most widely used concrete frameworks OpenMP and MPI as well as the threading interface pthreads for writing parallel programs for either shared or distributed memory parallel computers with emphasis on general concepts and principles. Code examples are given in a C-like style and many are actual, correct C code. The lecture notes deliberately do not cover GPU architectures and GPU programming, but the general concerns, guidelines and principles (time, work, cost, efficiency, scalability, memory structure and bandwidth) will be just as relevant for efficiently utilizing various GPU architectures. Likewise, the lecture notes focus on deterministic algorithms only and do not use randomization. The student of this material will find it instructive to take the time to understand concepts and algorithms visually. The exercises can be used for self-study and as inspiration for small implementation projects in OpenMP and MPI that can and should accompany any serious course on Parallel Computing. The student will benefit from actually implementing and carefully benchmarking the suggested algorithms on the parallel computing system that may or should be made available as part of such a Parallel Computing course. In class, the exercises can be used as basis for hand-ins and small programming projects for which sufficient, additional detail and precision should be provided by the instructor.