Gamma ray bursts (GRBs) are short bursts of high energy γ-radiation and are among some of the most energetic phenomena
in the universe. GRBs have three distinct emission phases: the prompt phase with high-energy γ-rays, the precursor phase
which is the time interval before the prompt phase and is reported to have an additional smaller burst for some GRBs,
and the afterglow phase which is the time interval after the prompt phase with observations for electromagnetic radiation
across a large wavelength range reported for many GRBs. GRBs have long been considered as a possible source of ultra
high energy cosmic rays, which makes them a promising neutrino source candidate. Unlike cosmic rays, neutrinos interact
only weakly, allowing them travel unabsorbed by intervening matter and undeflected by magnetic fields, so their arrival
directions at Earth point straight back to their origins. The work presented in this thesis searches for correlations between
GRBs and some of the high energy neutrinos detected by the IceCube Neutrino Observatory (IceCube), the most sensitive
instrument to date to detect high energy astrophysical neutrinos.

Previous IceCube searches for neutrino correlations with GRBs focused on the prompt phases of the GRBs and found
no significant correlation between neutrino events and the observed GRBs. This motivates us to extend our search beyond
the prompt phase. A model-independent search using an unbinned maximum likelihood method is performed to investigate
muon neutrino correlations with the precursor and afterglow phases of gamma ray bursts and the results are presented.
The analysis is applied to a selection of 733 GRBs searching for neutrino correlations separately for the precursor and the
prompt+afterglow emission regions and the best-fit results are obtained for individual GRBs for each search. The final
significance for each search is evaluated using binomial tests. Neither of the two searches provides significant evidence
of neutrino emission from GRBs during an extended time period up to two weeks before or after the prompt phase of
γ-ray emission and the top 20 results for each search along with the fitted parameters are presented in this thesis. The
analysis results are used to constrain the contribution of the cosmic GRB population to the diffuse astrophysical neutrino
flux observed by IceCube. The emission on timescales up to 104 s is constrained to 24% of the total diffuse flux, and the
results covering a range of emission timescales is presented.

The performance of Machine Learning based reconstruction methods is also discussed with a focus on the Deep Neural
Network (DNN) algorithms currently being developed in IceCube. The preliminary results highlight the potential of DNNs
to improve upon the existing direction reconstruction methods for high energy track-like neutrino events.