Smarandache developed hypersoft set theory as an extension of soft set theory, to adequate the existing concept of soft set for multi-attribute function. In this study, essential elementary properties e.g. not set, subset, absolute set, and aggregation operations e.g. union, intersection, complement, AND, OR, restricted union, extended intersection, relevant complement, restricted difference, restricted symmetric difference, are characterized under hypersoft set environment with illustrated examples. New notions of relation, function and their basic properties are also discussed for hypersoft sets. Moreover, matrix representation of hypersoft set is presented along with different operations. Lastly, some new hybrids of hypersoft set are also presented for further extension in different directions.