Advancements in spectroscopy rely on the improvement of two fundamental characteristics: spatial and temporal resolutions. High harmonic spectroscopy (HHS) is an emerging technology that promises the capability of studying the fastest processes that exist today: electronic motion with angstrom spatial and attosecond temporal resolution. HHS is based on the process of high harmonic generation (HHG) which arises from the nonlinear interaction between an intense, infrared laser pulse and an atomic or molecular gaseous medium, producing coherent, attosecond-duration bursts of extreme ultraviolet (XUV) light. In order to utilize the attosecond pulses for spectroscopic measurements, it is necessary to improve the conversion efficiency of HHG. Chapter 2 of this thesis describes the improvements we make to the HHG source in order to obtain high XUV photon flux and we report on the nonlinear ionization of atomic systems using these pulses in Chapter 6. In Chapters 3 - 5, we describe several HHG experiments in complex, polyatomic molecules in order to promote the use of HHS as a general spectroscopic tool. Amplitude modulations in high harmonic spectra of complex molecules can be attributed to several types of interference conditions that depend on a system's molecular or electronic structure such as recombination with multiple centres or dynamical interference from multi-orbital contributions to ionization. Our results demonstrate the capability of HHS to extract useful information on molecular and electronic structure from large, polyatomic molecules directly from their high harmonic spectra. Furthermore, we use HHS to investigate the suppression of ionization in complex molecules due to quantum destructive interference during ionization as well as the distinguishability of emitted harmonic spectra from molecular isomers. Chapter 6 explores the study of multi-electron dynamics in complex molecules using XUV multiphoton ionization of atoms and molecules as well as the ionization and fragmentation of C60 which has hundreds of delocalized valence electrons. This thesis also describes the author's role in the design and fabrication of a time-of- flight mass spectrometer (Section 6.1) as well as an HHG detector system (Appendix A).