Under the standard Flat-ΛCDM cosmology, recent data suggests that the overall energy budget of our universe is split into Ωm ≈ 0.3, with Ωb/ΩCDM ≈ 0.19, according to sound horizon measurements. While the baryonic sector contributes only ∼ 15% of the total matter, it consists of a variety of particles as predicted in the Standard Model of particle physics. Hence, it is unsurprising that the remaining ∼ 85% cold dark matter (CDM) is also made up of multiple components that are cold and weakly interacting at large scales.

In this thesis, I attempt to separate these CDM components by exploiting scaledependent behaviors imprinted on the matter power spectrum, and their subsequent nonlinear evolution to amplify these signatures. They provide rich phenomenologies imprinted on the large-scale structures. Furthermore, the thesis would centered on studying the structures within dark matter haloes, where interactions among dark matter are encapsulated in the formation of stable haloes.

Particularly, the thesis would extensively focus on the use of gravitational lensing to deliver constraints on dark matter properties. To accurately account for increasingly complicated dark matter models, in this thesis, the first goal is to develop model-independent methods to characterise the gravitational lens system, so that generic constraints can be derived to exclude a class of dark matter models, instead of tailor-made constraints of very specific model. Furthermore, for the consistency with the observed large scale structures, many popular models predict the production of small scale, sub-resolutional dark matter sub-structures. In this thesis, I explored a generic framework to achieve super-resolution for gravitational lensing. To address these two goals, a prototype algorithm to constrain sub-resolutional dark matter substructures in a model-independent fashion is developed in the thesis. As far as we are aware of, this is the first algorithm ever proposed that achieves both the model-independent and the super-resolution requirements. Lastly, the computational aspect of gravitational lensing is explored in order to better quantify the numerical systematics involved in computational lensing, which is a premise required for robust characterisation of dark matter.