This thesis presents the development of a high school-level astrophysical sciences course, designed as an extracurricular for students with an interest in astronomy. Since astrophysics is rarely included in standard high school curricula, this set of lesson plans stands as an extracurricular option: an accessible, noncalculus-based entry point for students from diverse academic backgrounds. Its primary aim is not necessarily to prepare for advanced study, but rather to cultivate scientific literacy and understanding of core concepts of astrophysics, cross-cutting ideas, and real-world applications. This set of lesson plans is informed by contemporary pedagogical research, with an emphasis on student-centered learning and the use of play as a mode of academic engagement.

Asteroseismology is an important tool for probing the fundamental characteristics of pulsating stars. Stellar oscillations are influenced by internal pressure, temperature gradients, and the structure of convective zones. Therefore, studying these oscillations enhances our understanding of stellar interiors. Research has shown that high mass main sequence stars exhibit strong pulsations. Theoretical models predict that low mass stars including M dwarfs can also pulsate at shorter periods and lower amplitudes. However, previous Kepler and K2 missions failed to detect convincing pulsations in M dwarfs likely due to a combination of instrumental limitations and the intrinsic faintness of the signals. In this work, we aim to identify solar like pulsations in low mass stars, particularly M dwarfs, using the Transiting Exoplanet Survey Satellite (TESS) 20 second cadence data. The high cadence and improved photometric precision of 20 second cadence data provide our best current opportunity to detect these faint pulsations especially in the low frequency, low amplitude regime where they are expected to occur. We extracted and analyzed light curves from our target stars to identify and characterize noteworthy signals. After processing the data, we used Lomb Scargle periodograms, power spectrum, and threshold analysis to investigate the nature of these signals. Our analysis revealed a variety of phenomena, including stellar flares, eclipsing binaries, variable stars, previously uncatalogued pulsations from nearby higher mass stars, and strong rotational modulation signatures in many of our targets.

The Rubin Observatory Legacy Survey of Space and Time (LSST) is projected to discover hundreds of gravitationally lensed Type Ia supernovae (glSNe), offering an unprecedented opportunity for time-delay cosmography and independent measurements of the Hubble constant. However, the majority of Rubin-discovered glSNe will be marginally resolved in ground-based imaging, making accurate deblending of the multiply-imaged supernovae from the foreground lens and host galaxy a critical challenge. We present a new framework to extract light curves of the multiply-imaged SNe from blended glSNe systems via joint forward modeling of multi-epoch, multi-band high-resolution space-based imaging and ground-based imaging using \texttt{Scarlet2}, combined with Gaussian Process time-delay inference using \texttt{GausSN}. Using pixel-level simulations of Rubin and Roman imaging of typical glSNe systems from the Goldstein et al. 2019 catalog across a range of angular separations, we quantify pipeline performance as a function of source blending and space-based follow-up availability. We find that Rubin-only observations are sufficient to recover time-delays with sub-day mean errors, outperforming configurations that include supplemental Roman epochs. SN image separations are recovered to $\sim 10-2$ arcsecond precision even when sources are initialized with significant spatial offsets. These results suggest transient light curves, time-delays, and image positions can be extracted from Rubin data alone, while more accurate lens mass modeling can be performed separately using archival high-resolution imaging, reducing the need for prompt space-based follow-up and substantially increasing the number of systems suitable for time-delay cosmography.

General relativity represents one of the most successful physical theories ever constructed, redefining gravity not as a force but as the curvature of spacetime itself. Nowhere in the cosmos is this success more dramatic, or more challenged, than in the theory's prediction of black holes. This thesis traces the development of gravity from Newtonian mechanics to Einstein's geometric framework, showing how general relativity triumphantly explains gravitational phenomena while predicting its own breakdown under extreme conditions. Understanding how black holes simultaneously confirm and destabilize general relativity is essential for clarifying why the search for a quantum theory of gravity is not speculative, but logically forced by the structure of our best classical theory.

Beginning with Newtonian gravity, the thesis establishes the conceptual assumptions of absolute space, absolute time, and a force-based interaction between objects before showing how empirical and theoretical tensions motivated Einstein's radical reformulation of the theory. The geometric structure of general relativity is then introduced through the Einstein field equations and the geodesic motion of matter, demonstrating how gravity emerges from a curvature of spacetime rather than physical force. Exact solutions to these equations, notably the Schwarzschild and Kerr metrics, give rise to black holes, revealing concepts such as event horizons, strong-field effects, and an unexpected simplicity captured by the ``no-hair'' theorem.

The thesis next follows the transition of black holes from mathematical curiosities to astrophysical realities, making true the physical triumph of general relativity. Observational evidence from X-ray binaries, stellar orbits around Sagittarius A*, gravitational-wave detections, and black hole imaging demonstrates that general relativity accurately describes black holes in the observable strong-field regime. These empirical feats confirm the Kerr description of black holes while simultaneously highlighting a profound limitation: all observations are restricted to the exterior spacetime, leaving the interior singularity fundamentally untested.

At the core of every classical black hole lies a singularity: a region where spacetime curvature diverges and general relativity loses predictive power. Through the singularity theorems, cosmic censorship, and the black hole information paradox, this thesis argues that singularities represent not empirical failures but internal inconsistencies in the theory itself. The combination of singularities and Hawking radiation exposes a deep conflict between general relativity and quantum mechanics, indicating that Einstein's theory is incomplete rather than incorrect.

Finally, this thesis will explore how black hole thermodynamics, horizon entropy, and holographic ideas suggest a new perspective in which spacetime and gravity emerge from underlying quantum degrees of freedom. In this view, black holes are not merely endpoints of classical physics but gateways to a deeper understanding of quantum spacetime. By examining black holes as both confirmations and stress tests of general relativity, this work positions them as central objects in the ongoing search for a quantum theory of gravity.

This thesis explores a fundamental question about dark matter: where is it distributed in the Universe? Is it found primarily with the halos of individual galaxies which are then assembled into groups, clusters, and the large-scale structure of the Universe or does a substantial diffuse component exist beyond these halos?

We use the mass-to-light ratio ($M/L$) as a diagnostic across cosmic scales. We begin by calibrating galaxy-scale $M/L$ ratios for $L\ast$ spiral and elliptical galaxies using multiple independent approaches including dynamical mass estimates for the Milky Way and Andromeda compiled from the literature, weak gravitational lensing measurements from the Dark Energy Spectroscopic Instrument (DESI) and the Dark Energy Survey (DES) extending into the dwarf galaxy regime, and stellar-to-halo mass constraints from the Cosmic Evolution Survey (COSMOS) survey. We also calibrate a luminosity-dependent $M/L$ relation, which is then integrated over the Schechter galaxy luminosity function to predict the total $M/L$ expected from galaxy halos alone.

The predicted galaxy halo $M/L$ is compared to observational measurements of groups and clusters to assess whether galaxy halos alone can account for the dark matter we observe at larger scales. Our results are consistent with the dark matter content on all cosmic scales, with no compelling evidence found for the presence of dark matter beyond what is accounted for by the assembly of galaxy halos. We explore the sensitivity of our predictions to the spread in dynamical mass estimates for anchor galaxies like the Milky Way and Andromeda, the choice of faint-end slope $\alpha$ in the luminosity function, the assumed galaxy morphology-density relation, the treatment of $M/L$ at the bright end, and more.