Many of the most important functions performed by nucleic acids are highly dynamic, whether in natural biological roles or in the field of DNA based nanotechnology. Despite a secure understanding of the thermodynamics of hybridization, the kinetics and particularly the dynamics remain less well understood. The fundamental structural transition that underlies much of nucleic acid folding is the formation of base pairs mediated by hydrogen bonding between complementary nucleobases and by stacking interactions with neighboring bases along the strand. To advance our understanding, an experimental approach that possesses both high time resolution and structural sensitivity towards these fundamental interactions is required. The work in this thesis develops a strategy for addressing DNA structural dynamics and hybridization kinetics through steady-state and transient temperature jump (T jump) nonlinear infrared (IR) spectroscopy since the molecular vibrations probed are sensitive to the hydrogen bonding and base stacking interactions that mediate nucleic acid folding. In particular, two-dimensional infrared (2D IR) spectroscopy offers sub picosecond time resolution and enhanced structural sensitivity through cross-peak information that reveals the coupling between nucleobase vibrations. By studying a model set of DNA oligonucleotides in which the placement of guanine-cytosine (GC) base pairs is varied in an otherwise adenine-thymine (AT) sequence, an assembly of IR experimental and analysis methods reveals sequence-dependent variation in the ensemble of hybridized duplex structures. A simple statistical lattice model is developed that provides an intuitive interpretation of the experimental results. Transient T-jump experiments that track the dehybridization of the DNA double helix in real-time between nanoseconds to milliseconds resolve essentially barrierless unzipping dynamics as the terminal base pairs fray as well as activated barrier crossing between the duplex and single strand states. Once validated on studies of model canonical oligonucleotides, the approach developed in the first half of the thesis is applied to investigate naturally occurring non-canonical nucleobases implicated in epigenetic regulation of the mammalian genome. Specifically, modified deoxycytidines that result from methylation of the 5 position of cytosine (mC) followed by successive oxidation of the methyl group to 5-hydroxymethyl- (hmC), 5-formyl- (fC), and 5 carboxyl- (caC) cytosine are involved in the active DNA demethylation cycle, which is central to gene regulation and cellular development. The influence of each of these modified nucleobases on the fundamental biophysical properties of DNA as well as the potential biological implications of such effects remains a topic of ongoing debate. The latter half of the thesis seeks to address some of these unresolved questions. 2D IR measurements reveal that the canonical keto amino tautomeric form predominates for fC and caC under physiological conditions, ruling out the possibility that the formyl and carboxyl groups shift the tautomeric equilibrium and thereby disrupt base pairing. Proposed weakened base pairing in oligonucleotides containing fC and caC is supported by observations of increased acidity at the cytosine N3 hydrogen bond acceptor site as well as altered stability in fC and caC containing duplexes. Finally, the impact of each of the cytosine derivatives on the kinetic barrier to opening modified base pair domains is characterized by T jump measurements, revealing a significant reduction in the dissociation barrier for base pairs involving fC and hmC while both mC and caC show a minor reduction in barrier height relative to canonical C. Possible biological implications of these trends are discussed.