  Part I describes the analysis of periodic and transient signals in EGRET
data. A method to search for the transient flux from gamma-ray bursts
independent of triggers from other gamma-ray instruments is developed. Several
known gamma-ray bursts were independently detected, and there is evidence for a
previously unknown gamma-ray burst candidate. Statistical methods using maximum
likelihood and Bayesian inference are developed and implemented to extract
periodic signals from gamma-ray sources in the presence of significant
astrophysical background radiation. The analysis was performed on six pulsars
and three pulsar candidates. The three brightest pulsars, Crab, Vela, and
Geminga, were readily identified, and would have been detected independently in
the EGRET data without knowledge of the pulse period. No significant pulsation
was detected in the three pulsar candidates. Eighteen X-ray binaries were
examined. None showed any evidence of periodicity. In addition, methods for
calculating the detection threshold of periodic flux modulation were developed.
The future hopes of gamma-ray astronomy lie in the development of the Gamma-ray
Large Area Space Telescope, or GLAST. Part II describes the development and
results of the particle track reconstruction software for a GLAST science
prototype instrument beam test. The Kalman filtering method of track
reconstruction is introduced and implemented. Monte Carlo simulations, very
similar to those used for the full GLAST instrument, were performed to predict
the instrumental response of the prototype. The prototype was tested in a
gamma-ray beam at SLAC. The reconstruction software was used to determine the
incident gamma-ray direction. It was found that the simulations did an
excellent job of representing the actual instrument response.
