Various theoretical considerations suggest that baryon number should be violated. Nucleon decay, which typically appears within the context of unified theories, would provide a definitive signature of baryon number violation. In this dissertation, we report on the search results for $p \rightarrow e^+X$, $p \rightarrow \mu^+$ (where $X$ is an invisible, massless particle), $n \rightarrow \nu\gamma$, $p \rightarrow e^+\nu\nu$, $p \rightarrow \mu^+\nu\nu$, $np \rightarrow e^+\nu$, $np \rightarrow \mu^+\nu$ and

$np \rightarrow \tau^+\nu$ nucleon and dinucleon decays at the Super-Kamiokande experiment. Some of these searches are novel. Using data from a combined exposure of 273.4 kton$\cdot$years and a $\chi^2$ spectral fitting technique, a search for these decays yields a result consistent with no signal. Accordingly, lower limits on the partial lifetimes of $\tau_{p \rightarrow e^+ X} > 7.9 \times 10^{32}$ years, $\tau_{n \rightarrow \nu\gamma} > 5.5 \times 10^{32}$ years, $\tau_{p \rightarrow \mu^+ X} > 4.1 \times 10^{32}$ years, $\tau_{p \rightarrow e^+\nu\nu} > 1.7 \times 10^{32}$ years, $\tau_{p \rightarrow \mu^+\nu\nu} > 2.2 \times 10^{32}$ years, $\tau_{np \rightarrow e^+\nu} > 2.6 \times 10^{32}$ years, $\tau_{np \rightarrow \mu^+\nu} > 2.0 \times 10^{32}$ years and

$\tau_{np \rightarrow \tau^+\nu} > 3.0 \times 10^{31}$ years at a 90\% confidence level are obtained. These results provide stringent test of new physics and also limit the parameter space of models that allow for such processes.

Non-Standard Interactions (NSI) between neutrinos and matter affect neutrino flavor oscillations.

Due to the high matter density in the core of the Sun, solar neutrinos are well suited to probe these interactions.

Using the 277 kton-yr exposure of Super-Kamiokande to $^{8}$B solar neutrinos, we search for the presence of NSI.

Our data favors the presence of NSI with down quarks at 1.8$\sigma$, and with up quarks at 1.6$\sigma$, with the best-fit effective NSI parameters being ($\epsilon_{11}^{\textrm{d}},\epsilon_{12}^{\textrm{d}}$) = (-3.3, -3.1) for d-quarks and

($\epsilon_{11}^{\textrm{u}},\epsilon_{12}^{\textrm{u}}$) = (-2.5, -3.1) for u-quarks.

After combining with data from the Sudbury Neutrino Observatory and Borexino, the significance increases by 0.1$\sigma$.

Solar neutrinos pass through the Earth's surface with a flux on the order of $10^{11} /\mbox{cm}^2/s$. The Super-Kamiokande (SK) searches for neutrinos from the sun with an energy above 4.0 MeV. Neutrinos rarely interact with matter, and removing backgrounds that would otherwise overwhelm the signal is imperative. SK observes about 2 muons a second at its depth of 2700m water equivalent, and a fraction of these muons shower within the detector with a possibility to create radioactive isotopes (spallation) which live from milliseconds to tens of seconds. Radioactive isotopes from any source are by far the largest source of background in the solar neutrino energy region observed in SK, and spallation is the dominant background to neutrino interactions between 6 and 20 MeV. Spallation in SK is mostly caused by neutrons and pions interacting with the Oxygen nucleus. Recently, new techniques involving identifying neutron in the showers after muons and effective tagging of multiple spallation, along with improvements and additions to former spallation tagging methods have reduced deadtime by $\sim$55\% ($\sim$45\%) where neutron data is available (unavailable). This increases measured solar neutrino signal by 12\% and reduces relative statistical error by 6.6\% for the entire SK-IV solar neutrino sample.