This dissertation presents my research work with the ATLAS experiment at the Large Hadron Collider (LHC). The LHC is built in a circular tunnel of27km in circumference buried around50to175m underground and straddles the Swiss and French borders on the outskirts of Geneva. It is designed to produce proton-proton collisions at center-of-mass energy (CME) of14TeV with peak luminosity of1034cm-2s-1. ATLAS is a particle physics experiment at the LHC. The ATLAS detector is a state of art general purpose detector with almost4π coverage to detect particles created in the proton-proton collisions from the LHC. The LHC is a dream machine for particle physicists to create particles that existed about0.001ns after Big Bang, the start of the universe. Research conducted in experiments at the LHC will significantly advance our understanding how our universe works at its most fundamental level. My thesis work has focused on studies of the vector boson pair, W±Z, productions at the LHC to search for new physics through the measurements of the W±Z production cross-section and the triple-gauge couplings.The LHC and the ATLAS detector have been operated remarkably since fall of2009. The peak luminosity of the LHC increased from2x1029cm-2s-1to7.7×1033cm-2s-1, more than4orders of magnitude increase over past three years. With over93%data taking efficiency, ATLAS has collected data with an integrated luminosity of5fb-1at7TeV in2011, and15fb-1at8TeV up to Sept.2012. Using data collected in2011this thesis work has made the first measurement at the LHC on W±Z production cross-section, which is one of the major milestones of the LHC physics programs as the steppingstone for discovery of new physics at TeV energy scale. Using this data-set, the most stringent limits on the anomalous triple gauge boson couplings (TGCs) of the WWZ vertex are set. The massive new resonance productions are searched in the WZ mass spectrum. No evidence of new physics beyond the standard model (SM) is observed.The measurements of the WZ production cross-section provide a test of the non-Abelian SU(2)×U(1) gauge structure of the SM electroweak theory, and the understanding of the background for the Higgs searches. The WZ production cross section is measured from leptonic decay channels, namely the combination of Z→ee (μμ) and W→eve (μvμ): eeev, eeμv, evμμ and μμμv final states. Major background of this measurement comes from other physics processes, such as ZZ, Z+jets and Top. Data-driven method is developed to estimate the background contributions from Z+jets and Top, while The background from ZZ is estimated from MC simulation. The total WZ production cross-section is measured to be19.0-1.3+1.4(stat)±0.9(syst.)±0.4(lumi.) pb, based on total317events selected from data and68±10estimated background. The uncertainty of the measurement is much smaller as compared to that of previous measurements from Tevatron at1/2s=1.96TeV.The measurements of TGCs provide a sensitive probe for new physics at high energy scale beyond the SM. The anomalous triple gauge boson couplings (aTGC) are probed from the WZ events by comparing the observed transverse momentum spectrum of the Z boson with that of the theoretical predictions with aTGC. Data agree with the SM prediction from the likelihood fit, which results in confidence intervals at95%C.L. on aTGC as△g1Z∈[-0.057,0.093],△kZ∈[-0.37,0.57] and λZ∈[-0.046,0.047]. These limits are much more stringent compared to the previous measurements at Tevatron.Many physics models predict new particles decaying to WZ final state. A search for high mass WZ resonance is carried out using the same data-set. The invariant mass of the WZ system is reconstructed using measured energies and momenta of leptons and missing energy constrained to the W mass. To avoid event selection bias, a blinded analysis approach is used. In this analysis a control region is defined, where potential new physics signal is minimal. Only when the principal background from the known physics process is understood in the control region we unblind the analysis in the signal region to search for new resonance. No new physics is observed in the signal region. The result is interpreted as cross-section limits on new gauge boson W’ from Extend Gauge Models (EGM) and ρτ from Low Scale Technicolor model (LSTC). The lower limit on W’ mass is1.1TeV, and580GeV for ρτ at95%C.L.Searching for new physics at the LHC is still at its early stage in terms of luminosity and energy of the LHC. The methods and techniques developed in this thesis work have paved the way for the continued searches with ATLAS experiment at the LHC.