The emerging field of silicon photonics enables the fabrication of on-chip, ultrahigh bandwidth optical networks which are critical for the future of microelectronics. One of the bottlenecks for multi-core, multi-processor electronics is the on-chip copper wire interconnect network. Integrated photonics seek to transfer the data transmission from the electrical domain to the optical domain just as fiber has done for long haul communications. Nonlinear optics has a role to play in providing some of the necessary components for such a network. Silicon has emerged as a key material for integrated photonics due to the CMOS processing capabilities, its high index contrast, electro-optic properties and strong nonlinearity. However, silicon experiences severe nonlinear losses which limit the efficiency of processes such as four-wave mixing and Raman amplification. This dissertation examines a new material platform for integrated nonlinear photonics by developing silicon nitride waveguides and resonators. We start with background information on the field and motivation for integrated photonics and nonlinear optics. We then develop a theoretical foundation for optical waveguides and ring resonator devices by deriving the key governing equations and parameters. The material properties and fabrication techniques are described in detail and we are able to measure the nonlinear refractive index of silicon nitride through the nonlinear self-phase modulation. We explore the process of four-wave mixing in waveguides to demonstrate efficient wave- length conversion and parametric gain. By leveraging the parametric gain and high quality factor resonators, we demonstrate the first fully integrated optical parametric oscillation and frequency comb generation. We go on to show one of the potential applications of this device as a multiple wavelength source for wavelength division multiplexed optical networks. We also discuss harmonic generation in which infrared light is converted to visible wavelengths. We exploit an interface effect to induce the second order nonlinearity in the material which could enable a host of other nonlinear process previously inaccessible to CMOS-compatible photonics. In the summary we discuss a wide array of future work that could build on the material presented here.