In this project, we have undertaken studies aimed at a better understanding of the theory of scalarHiggs bosons. Two representative models which go beyond the Standard Model (SM) of elementaryparticles are considered, namely the triplet model (HTM) and the Left-Right symmetric model in itsminimal version (MLRSM). Both models predict the existence of not only neutral scalar particles butalso doubly charged scalars H±± (doubled elementary charge |e|). Scalar Higgs bosons are spinlessparticles and are responsible for the mechanism of mass generation of leptons, quarks and particularly gauge bosons. We observed the elementary scalar particle for the first time in 2012 at the LHCaccelerator, which confirmed that the theory based on Higgs particles’ interactions is correct. Searching for non-standard Higgs particles is vital for studying the shape of the Higgs potential. It determines the mechanism of the mass generation for leptons, quarks and gauge bosons and is also veryimportant in cosmology regarding the evolution of the Universe and its ultimate stability. Furthermore, the observation of doubly charged scalar particles H±± could be associated with the so-called leptonflavour violating (LFV) processes. For example, H±± can interact with muons in non-standard theoriesand LFV undetected so far processes like muon radiative decays μ→eγ are possible.In the project, we have analysed both correlations among model parameters and limits on theirvalues coming from current experimental data and lack of the observation of LFV processes. These studies are essential for the prediction of possible signals at high energy accelerators. The main goal of the study was a precise analysis of the H++H-- pair production in e+e- and pp (proton-proton) collisions and their further decays. Notably, the Principal Investigator (PI) has studied in details leptonic decays of doubly charged scalar particles. Those production and decay processes can give us potentially the clearest signals of four charged leptons without missing energy. Because the H±± masses are limited due to lack of detection of the doubly charged scalar particles at LHC (pp collisions), the energy needed to study their production at the e+e- colliders has to be very high (1500 GeV). That energy range is considered only by the CLIC collaboration at CERN. However, regarding the pp→H++H-- process, the energy 14 TeV available at the LHC is sufficient for their studies. LHC works at 14 TeV, which will be upgraded (so-called HL-LHC) and will start collecting data in 2021. We have also prepared computations for the future pp accelerator with the energy 100 TeV, planned to bebuilt at CERN too (so-called FCC-hh). Our studies show that the existing bounds on the model parameters from the analysis of available experimental data limit the possibility of detection of the H±± particles dramatically. For example, within the HTM model neutrino mass and mixing data rules out substantial contributions to the H±± pair production from the so-called t-channel, which could dominate over the resonance s-channels otherwise. We have shown that the kinematic cuts on the detector signal can lead to the situation that four muon production processes are negligible within the HTM, and they are significant within MLRSM, so the detection of that signal may distinguish between those two models. We have estimated that the aggregate signal within the MLRSM in the e+e- collider for four muon production and the H±± mass equal to 700 GeV might reach 205 events, in comparison to the SM background at the level of 8 events. In the case of the hadronic collider, the highest aggregate signal at the HL-LHC (FCC-hh) for four muon production coming from the decay of H±± with mass 1000 GeV can reach 112 (52 540) events,with the SM background at the level of 77 (15 167) events.As a result of the project, we have prepared two scientific articles; one has been published in the Symmetry journal https://www.mdpi.com/2073-8994/12/1/153, another is publicly available in arXiv https://arxiv.org/abs/2006.04610 and sent for publication to one of the specialized journals. Besides, the leader of the project has presented the results of the study on 12 conferences and seminars, domestically and abroad (Katowice, Kraków, Wrocław, Warszawa, Austria, Germany, Portugal,Switzerland, Italy). Links are available below. The results of the grant will be the basis for the PhD dissertation by the PI.