Synthesis programs:

Pure Data
graph-based sound language public domain. libpd-- turns PD into a signal processing library.

MaxMSP
graph-based sound language, commercial product

SuperCollider
client-server based sound synthesis language

CSound
well-known synthesis language

The Synthesis ToolKit in C++ (STK)
physical modeling toolkit

athenaCL
modular poly-paradigm algorithmic music composition in a cross-platform interactive command-line environment.

Sound Processing Kit

CREATE Signal Library

SonicFlow

Sig++: Musical Signal Processing in C++

ChucK
Strongly-timed, Concurrent, and On-the-fly Audio Programming Language

The Wekinator
Software for using machine learning to build real-time interactive systems

Puredyne is the USB-bootable GNU/Linux operating system for creative multimedia

liblo is an implementation of the Open Sound Control protocol, for communication among computers, sound synthesizers, and other multimedia devices. Introduction.

Lecture notes:

Introduction-Computer Audio Overview

Introduction to Pure Data (PD)

Musical Interface Design

Physical Modeling- waveguides