Supersymmetric extensions to the standard model

can solve a number of current, unresolved issues in particle physics.

In most of these models, the top-squark,

the supersymmetric partner to the top quark,

plays an integral role in fixing some of these issues.

Although the existence of many supersymmetric particles

have been strongly constrained by experiments,

currently the existence of the top-squark remains largely unconstrained.

This dissertation presents several searches for top-squark pair-production

in $R$-parity conserving supersymmetry where the lightest neutralino is assumed to be stable.

The data utilized in this search corresponds to 19.66 fb$^{-1}$ of proton-proton collision data collected

by the CMS experiment at $\sqrt{s} = 8$ TeV during the 2012 LHC run.

The main focus of the dissertation is a search in the dileptonic final state,

where the experimental final state is two leptons, two bottom quarks, and missing transverse momentum.

Using a cut-based approach, no excess of events above the nominal background expectations is observed.

This result is combined with a top-squark search in the semi-leptonic final state

to exclude top-squark pair-production at the 95% confidence level for top-squark masses up to 700 GeV.

when the lightest neutralino's mass is below 260 GeV.

This dissertation also presents a powerful new approach to the dileptonic top-squark search.

Shape-based comparisons, using three complementary discriminating variables,

between the observed data and the nominal background expectations

achieve much better statistical sensitivity to top-squark pair-production

in comparison with the cut-based search.

Notably, the shape analysis excludes the existence of top-squarks

that are nearly mass-degenerate with the top quark.

Currently, no other direct top-squark search can achieve this exclusion.

As well, there are a number of observed excesses in the shape analysis.

The statistical significances of these excesses are tested

against top-squark pair-production models.

The subset of models where top-squark decays to a top quark and the lightest neutralino

and the mass-splitting between the top-squark

and the lightest neutralino is $(150\pm12.5)$ GeV are found to fit

with a statistical significance of $\sim 3.5$--$4\sigma$.

The global significance of these excesses is quantified

by correcting for the look-elsewhere effect;

the highest post-correction significances are found to be $\sim 2.5$--$3\sigma$.