Magnetic Particle Imaging (MPI) is a novel biomedical imaging modality that shows great potential in terms of sensitivity, resolution, and contrast. Since its first introduction in 2005, several applications of MPI have already been demonstrated such as angiography, stem cell tracking, and cancer imaging. Recently, multi-color MPI techniques have been proposed to increase the functionality of MPI, where different nanoparticles are distinguished according to the differences in their responses to oscillating magnetic fields. These methods can also be extended to probe environmental factors such as viscosity and temperature, provided that the responses of different nanoparticles or nanoparticles in different environments are pre-calibrated. This thesis proposes a new multi-color MPI technique that does not require a calibration phase. This new technique directly estimates the relaxation time constants of nanoparticles to distinguish nanoparticle types and environmental factors from the MPI signal, and generates a multi-color relaxation map. The validity of the proposed technique is confirmed through an extensive experimental work with an in-house Magnetic Particle Spectrometer (MPS) at 10.8 kHz and an in-house MPI scanner at 9.7 kHz drive field frequencies, successfully distinguishing different nanoparticle types. The proposed calibration-free multi-color MPI technique is a promising method for future functional imaging applications of MPI.