Topological Microfluidics : Nematic Liquid Crystals and Nematic Colloids in Microfluidic Environment This work represents one of the first comprehensive attempts to seamlessly integrate two highly active interdisciplinary domains in soft matter science microfluidics and liquid crystals (LCs). Motivated by the lack of fundamental experiments Dr. Sengupta initiated systematic investigation of LC flows at micro scales gaining new insights that are also suggestive of novel applications. By tailoring the surface anchoring of the LC molecules and the channel dimensions different topological constraints were controllably introduced within the microfluidic devices. These topological constraints were further manipulated using a flow field paving the way for Topological Microfluidics. Harnessing topology on a microfluidic platform as described in this thesis opens up capabilities beyond the conventional viscous dominated microfluidics promising potential applications in targeted delivery and sorting systems self assembled motifs and novel metamaterial fabrications