<p> This thesis studies the optical and electronic compensation for fiber nonlinearities based on the theory of Volterra expression. Signals propagating through optical fibers suffer from both linear and nonlinear distortion. In this thesis, we first construct an approximate inverse of fiber systems based on the theory of pth-order inverse of Volterra expansion. For a fully dispersion compensated fiber system H with a second-order dispersion profile f32 (z) and a total length of L, if the input field is real, we show that the inverse can be approximated by a system K with an inverted seconder-order dispersion profile -/32 ( z-L), while keeping all the other parameters the same. We then further develop the scheme by adding an optical phase conjugator ( OPC) in the middle of the transmission line. More specifically, the inversion of a fully dispersion compensated N-span fiber system H with a second-order dispersion profile /32 (z) and a total length L, is realized using an OPC followed by another N-span system K with an inverted seconder-order dispersion profile -f32(z-L), while keeping all the other parameters the same. In this way the original input optical signals can be recovered exactly. Our analytical and numerical simulation results show that the scheme works well for both single-channel systems and WDM systems. For electronic compensation techniques, we examine a nonlinear intersymbol interference (ISI) canceler based on Volterra theory, which was proposed first for voiceband data transmission, and apply it to optical fiber systems here, for the first time to our knowledge. The canceler is able to compensate nonlinear ISI caused by the cross product of both precursor and post cursor. </p> / Thesis / Master of Applied Science (MASc)