Particles in the atmosphere are known to have negative health effects and important but highly uncertain impacts on global and regional climate. A majority of this particulate matter is formed through atmospheric oxidation of naturally and anthropogenically emitted gases to yield highly oxygenated secondary organic aerosol (SOA), an amalgamation of thousands of individual chemical compounds. However, comprehensive analysis of SOA composition has been stymied by its complexity and lack of available measurement techniques. In this work, novel instrumentation, analysis methods, and conceptual frameworks are introduced for chemically characterizing atmospherically relevant mixtures and ambient aerosols, providing a fundamentally new level of detailed knowledge on their structures, chemical properties, and identification of their components. This chemical information is used to gain insights into the formation, transformation and oxidation of organic aerosols. Biogenic and anthropogenic mixtures are observed in this work to yield incredible complexity upon oxidation, producing over 100 separable compounds from a single precursor. As a first step toward unraveling this complexity, a method was developed for measuring the polarity and volatility of individual compounds in a complex mixture using two-dimensional gas chromatography, which is demonstrated in Chapter 2 for describing the oxidation of SOA formed from a biogenic compound (longifolene: C15H24). Several major products and tens of substantial minor products were produced, but none could be identified by traditional methods or have ever been isolated and studied in the laboratory. A major realization of this work was that soft ionization mass spectrometry could be used to identify the molecular mass and formula of these unidentified compounds, a major step toward a comprehensive description of complex mixtures. This was achieved by coupling gas chromatography to high resolution time-of-flight mass spectrometry with vacuum ultraviolet (VUV) photo-ionization. Chapters 3 and 4 describe this new analytical technique and its initial application to determine the structures of unknown compounds and formerly unresolvable mixtures, including a complete description of the chemical composition of two common petroleum products related to anthropogenic emissions: diesel fuel and motor oil. The distribution of hydrocarbon isomers in these mixtures - found to be mostly of branched, cyclic, and saturated - is described with unprecedented detail. Instead of measuring average bulk aerosol properties, the methods developed and applied in this work directly measure the polarity, volatility, and structure of individual components to allow a mechanistic understanding of oxidation processes. Novel characterizations of these complex mixtures are used to elucidate the role of structure and functionality in particle-phase oxidation, including in Chapter 4 the first measurements of relative reaction rates in a complex hydrocarbon particle. Molecular structure is observed to influence particle-phase oxidation in unexpected and important ways, with cyclization decreasing reaction rates by ~30% and branching increasing reaction rates by ~20-50%. The observed structural dependence is proposed to result in compositional changes in anthropogenic organic aerosol downwind of urban areas, which has been confirmed in subsequent work by applying the techniques described here. Measurement of organic aerosol components is extended to ambient environments through the development of instrumentation with the unprecedented capability to measure hourly concentrations and gas/particle partitioning of individual highly oxygenated organic compounds in the atmosphere. Chapters 5 and 6 describe development of new procedures and hardware for the calibration and analysis of oxygenates using the Semi-Volatile Thermal desorption Aerosol Gas chromatograph (SV-TAG), a custom instrument for in situ quantification of gas- and particle-phase organic compounds in the atmosphere. High time resolution measurement of oxygenated compounds is achieved through a reproducible and quantitative methodology for in situ "derivatization"--Replacing highly polar functional groups that cannot be analyzed by traditional gas chromatography with less polar groups. Implementation of a two-channel sampling system for the simultaneous collection of particle-phase and total gas-plus-particle phase samples allows for the first direct measurements of gas/particle partitioning in the atmosphere, significantly advancing the study of atmospheric composition and variability, as well as the processes governing condensation and re-volatilization. This work presents the first in situ measurements of a large suite of highly oxygenated biogenic oxidation products in both the gas- and particle-phase. Isoprene, the most ubiquitous biogenic emission, oxidizes to form 2-methyltetrols and C5 alkene triols, while [alpha]-pinene, the most common monoterpene, forms pinic, pinonic, hydroxyglutaric, and other acids. These compounds are reported in Chapter 7 with unprecedented time resolution and are shown for the first time to have a large gas-phase component, contrary to typical assumptions. Hourly comparisons of these products with anthropogenic aerosol components elucidate the interaction of human and natural emissions at two rural sites: the southeastern, U.S. and Amazonia, Brazil. Anthropogenic influence on SOA formation is proposed to occur through the increase in liquid water caused by anthropogenic sulfate. Furthermore, these unparalleled observations of gas/particle partitioning of biogenic oxidation products demonstrate that partitioning of oxygenates is unexpectedly independent of volatility: many volatile, highly oxygenated compounds have a large particle-phase component that is poorly described by traditional models. These novel conclusions are reached in part by applying the new frameworks developed in previous chapters to understand the properties of unidentified compounds, demonstrating the importance of detailed characterization of atmospheric organic mixtures. Comprehensive analysis of anthropogenic and biogenic emissions and oxidation product mixtures is coupled in this work with high time-resolution measurement of individual organic components to yield significant insights into the transformations of organic aerosols. Oxidation chemistry is observed in both laboratory and field settings to depend on molecular properties, volatility, and atmospheric composition. However, this work demonstrates that these complex processes can be understood through the quantification of individual known and unidentified compounds, combined with their classification into descriptive frameworks.