Atomic force microscopy (AFM) is widely used to study material properties and domain heterogeneity of polymers. In both quasi-static force spectroscopy and dynamic AFM, challenging complexities such as the presence of different effective tip-surface forces, surface dynamics, and material viscoelasticity can occur on polymer samples. Many models that attempt to link experimental observables to contact mechanics fail to rigorously account for these complexities. This may lead to inaccurate and unreliable predictions, especially when examining soft polymers. Therefore, having access to rigorous models that can facilitate the understanding of the underlying phenomena during tip-surface interaction, explain the observations, and make reliable and accurate predictions, is of great interest. Among the previously developed models, Attard et al. proposed a novel non-Hertzian-based model that has a versatile ability to systematically incorporate different linear viscoelasticity constitutive models and surface adhesive forces. However, the implementation of Attard’s model into the AFM framework is challenging.<div><br></div><div>In a series of studies, we improve the computational speed and stability of Attard’s viscoelastic contact model and embed it into an AFM framework by proposing algorithms for three AFM operational modes: tapping mode, bimodal, and peak force tapping. For each mode, the results are successfully verified/validated against other reliable AFM codes, FEM simulations, and experiments. The algorithms’ predictions illustrate how viscoelasticity and surface adhesive hysteresis of polymeric samples is reflected in AFM observables. However, since Attard’s model does not lead to a closed-form solution for tip-surface interaction force, using that to quantify the surface mechanical properties based on the AFM observables is not straightforward. Therefore, we utilize the data analytics-based approaches such as linear regression and machine learning algorithms to enable the material viscoelasticity and adhesive parameters estimation based on the provided instrument observables.<br></div><div><br></div><div>The set of results reported in this thesis improves the current knowledge about complex phenomena that occur during tip-surface interactions, especially on soft-viscoelastic-adhesive polymers. The introduced “improved Attard’s model” fulfills the need for a continuum mechanics viscoelasticity contact model that rigorously captures the complexities of such samples. The viscoelasticity contact model and the proposed inverse solution algorithms in this thesis facilitate quantitative measurement and discrimination of the surface adhesive and viscoelastic properties based on the acquired nanoscale AFM maps of polymeric samples.<br></div>