The analysis presented in this thesis focuses on kinematic distributions in the t{bar t} system and studies in detail selected differential cross sections of top quarks as well as the reconstructed t{bar t} pair, namely the top quark transverse momentum and the t{bar t} system mass. The structure of the thesis is organized as follows: first the Standard Model of the particle physics is briefly introduced in Chapter 1, with relevant aspects of electroweak and strong interactions discussed. The physics of the top quark and its properties are then outlined in Chapter 2, together with the motivation for measuring the transverse top quark momentum and other kinematic-related variables of the t{bar t} system. The concepts of present-day high energy physics collider experiments and the explicit example of Fermilab Tevatron collider and the D0 detector in Chapters 3 and 4 are followed by the description of basic detector-level objects, i.e. tracks, leptons and jets, in Chapter 5; their identification and calibration following in next chapter with the emphasis on the jet energy scale in Chapter 6 and jet identification at the D0. The analysis itself is outlined in Chapter 7 and is structured so that first the data and simulation samples and the basic preselection are described in Chapter 8 and 9, followed by the kinematic reconstruction part in Chapter 10. Chapter 11 on background normalization and Chapter 12 with raw reconstructed spectra results (at the detector-smeared level) are followed by the purity-based background subtraction method and examples of signal-level corrected spectra in Chapter 13. Next, the procedure of correcting measured spectra for detector effects (unfolding) is described in Chapters 14-15, including migration matrix studies, acceptance correction determination as well as the regularized unfolding procedure itself. Final differential cross sections are presented in Chapter 16 with the main results in Figures 16.19-16.20. Summary and discussion close the main analysis part in Chapter 17, supplemented by appendices on the wealthy of analysis control plots of the t{bar t} → l + jets channel, selected D0 event displays and finally the list of publications and references. Preliminary results of this analysis have been documented in D0 internal notes [UnfoldTop], [p17Top], [p14Top]; as well as presented at conferences [APS08], [APS05]. The author has also been a co-author of more than 135 D0 collaboration publications since 2005. The author has taken part in the jet energy scale calibration efforts performing final closure tests and deriving a correction to jet energy offset due to the suppression of the calorimeter signal. The author has also co-performed the [phi]-intercalibration of the hadronic calorimeter and co-supervised the electromagnetic [phi]-intercalibration; recently has also been involved in maintaining the jet identification efficiencies measurement as a JetID convener. During the years in Fermilab, many events have taken place in the course of the analysis in persuasion, including more than 170 shifts served for the D0 detector with or without the beam, 168 talks presented with mixed results and reactions; and tens of thousands of code lines in C (and sometimes perhaps even really C++) written while terabytes of data were processed, analyzed, and sometimes also lost. It has been a long but profoundly enriching chapter of my life.