With the advent of Scanning Tunneling Microscopy (STM), the STM has provided us with unprecedented information on the electronic properties of a sample at the atomic level. Because of the STM's accessibility to the microscopic scale, an experiment on a macroscopic sample provides vast amounts of data. To understand the condensed matter physics underlying the vast STM data on a macroscopic sample, one needs analysis techniques for STM that make use of the aforesaid accessibility to the atomic scale. In this thesis, our aim is to devise analysis techniques that we term as "Inversion" techniques : a technique that extracts information regarding the Hamiltonian/physics of the sample from the STM data with minimal assumptions. In Chapter 2, we show that the local density of states (LDOS) measured in a STM experiment, at a single tip position contains oscillations as a function of energy, due to quasiparticle interference, which is related to the positions of nearby scatterers. We call them quasiparticle echoes. We propose a method of STM data analysis based on this idea, which can be used to locate the scatterers. In the case of a superconductor, the method can potentially distinguish the nature of the scattering by a particular impurity. In Chapter 3, we demonstrate an analysis scheme again based on quasiparticle interference around a point impurity, that extracts the lifetime of a quasiparticle by using the LDOS data around the impurity in a STM experiment. This data analysis scheme would augment the Fourier- Transform Scanning Tunneling Spectroscopic methods which provide us with the quasiparticle dispersion. Thus, point impurities can be used as probes to extract quasiparticle lifetimes from STM experiments and this would complement other experimental methods such as Angle Resolved Photo-emission Spectrocopy(ARPES). We explain in detail how the scheme works in the case of metals and outline the extension to the superconducting case. In Chapter 4, we deal with a specific part of STM phenomenology of the high temperature superconductor, Bi2 S r2Ca1Cu2 O8+ x . It concerns the high-energy features outside the gap seen in the STM experiments on BSCCO. Jinho Lee et al (Nature 442, 546 (2006)) showed that these features were a result of a bosonic mode's coupling to the electrons in the (believed to be) relevant CuO2 layer. The nature of the bosonic mode is still not resolved. Using a simplified model of d-wave BCS quasiparticles coupled to Einstein oscillators with a momentum independent electron-boson coupling, we try to answer : a) how to extract the frequency of the bosonic mode, and b) how to extract an estimate of the electron-boson coupling strength.