The main topic of this thesis is analysis of an unidentified Galactic TeV gammaray source, MGRO J1908+06, discovered by Milagro instrument in 2007. We analyzed 54 hours of observational data from the Very Energetic Radiation Imaging Telescope Array System (VERITAS), a ground-based gamma-ray observatory in southern Arizona comprised of an array of four Cherenkov Telescopes that reconstructs the energy and direction of astrophysical gamma-rays by imaging Cherenkov light emitted by energetic particles in air showers produced by the primary gamma-rays. MGRO J1908+06 is located between a supernova remnant SNR G40.5-0.5 and a young, energetic pulsar PSR J1907+0602. We studied the energy dependent morphology of the TeV emission from the source and measured the source extent and spectrum. The source extends well past the boundary of the SNR and is not correlated with strong radio continuum or molecular line emission which likely excludes an origin for the emission as solely due to the SNR. While emission in the 0.5-1.25 TeV band was centered around the pulsar, higher energy emission was observed near the supernova remnant. This morphology is opposite that observed in other pulsar wind nebulae. We proposed two models for the high energy emission located well away from the pulsar but close to the SNR: (1) shock acceleration at the shock front created by an interaction between the pulsar wind and the dense gas at the edge of the SNR or (2) molecular clouds around the SNR provides seed photons with energies higher than those from Cosmic Microwave Backgrounds for inverse Compton scattering. The former model can be tested by looking for molecular emission lines that trace shocks and by measuring the pulsar velocity. In addition, we investigated the gamma-ray emission from the nova explosion of V407 Cygni that occurred in March 2010. The Fermi-LAT observed this event in the energy range of E >100 MeV. The origins of the gamma-ray emission that the Fermi-LAT team proposed are either protons (hadronic model) or electrons (leptonic Allured, Thomas Brantseg, Casey DeRoo and Scott Griffiths. Lastly, I would like to express my special thanks to my family in Japan for their never ending encouragement and support.