Condensed matter physics in the 20^th Century was developed mostly for crystalline solids, and we know so little about the physics of liquids and glasses.  We do not even know how to describe the structure of these amorphous matters to discuss the structure-properties relationship, even though liquids and glasses are so important to everyday life.  This is because liquids and glasses are condensed matter with high density in which atoms are strongly correlated to each other.  Any theoretical effort runs into a thick barrier of many-body interactions.  To circumvent this difficulty the dynamics of a liquid is described usually by the continuum hydrodynamic theories with non-linear extension.  An alternative approach is to use the molecular dynamics (MD) simulation, taking advantage of recent progress in computing power.  However, MD simulations tend to leave us in a deluge of numbers, without a physical idea.  Our effort focused on breaking this conundrum by developing new concepts, using MD as a tool to shape the concept.  We introduced the idea of local topology of atomic connectivity, expressed in terms of the atomic level stresses.  We show that the macroscopic dynamics of a liquid and glass is directly connected to the local atomic dynamics in the form of topological excitations.  Characterization of these excitations leads to a better understanding of the glass transition and mechanical failure of a glass.