The atmospheric aerosol or particulate matter (PM) is one of the major issues of urban air quality affecting human and ecosystem wellbeing across the globe. APM consists of numerous particles of different sizes, ranging from ultra-fine particles up to particles with an aerodynamic diameter up to 10μm or larger. It has been reported that particulates less than 2.5μm are more hazardous due to their ability to penetrate deeper into human lungs and enter blood which may increase respiratory and cardiovascular morbidity compared to coarse particulates whose aerodynamic size is up to 10μm. The dynamics of atmospheric particulate matter (APM) are outcome of complex natural and anthropogenic contributors evolving with time, which cannot be analyzed using conventional time and frequency domain analysis techniques. For analyzing nonlinear dynamics of APM, various computational techniques have been used by researchers during last two decades to understand the dynamics of these systems. The research reported in this dissertation focused on quantifying the nonlinear dynamics of APM (fine and coarse particulates) in ambient air and indoor environment. The atmospheric particulate matter time series concentrations were acquired using EPAM-5000 monitor from the ambient air and indoor environment in the suburb of Muzaffarabad (Azad Jammu & Kashmir, Pakistan). The time series data of the particulates was then transferred to a computer for analysis. The behaviour and variability of PM2.5 and PM10.0 in the ambient and indoor environment were investigated by performing descriptive statistical analysis. The association between indoor and ambient particulates was examined using Pearson correlation analysis and regression analysis with ordinary least square method. Nonlinear time xvi series analysis techniques were used to characterize chaotic behaviour of the time series data. To capture nonlinear dynamics, phase space was reconstructed using an appropriate time delay and embedding dimension. The largest Lyapunov exponent (LLE) was computed to determine the evidence of deterministic chaos in the ambient PM time series data. The Hurst exponent was used to explore whether or not the APM time series data show persistent behaviour. The Poincare plot descriptors were used to show the short term, long term and point to point variability of the particulates. The permutation entropy (PE) which is a reliable measure in the presence of dynamical and observational noise was used for the examining the complexity of APM. Finally, graphical user interfaces (GUI) based software product was developed via a panel of computational techniques used in the research work. The statistical analysis of PM time series data indicated enormously higher mass concentrations of particulates in the ambient and indoor environment at all the sites. The results showed that the proportion of PM2.5 contained within PM10.0 was quite high depicting that fine particulates are major contributors of atmospheric PM in the Muzaffarabad city. Due to their ability of deeper penetration into the lungs, the higher proportions of fine particulates may cause hazardous effects on the people residing along the roadside. The optimum embedding dimension of reconstructed phase space at various time delays varied from 5 to 8 and 4 to 6 for PM10.0 and PM2.5 respectively. The higher values of optimal embedding showed that the mass concentrations of both particulates have more dominant degrees of freedom, indicating dynamically complex behaviour. The results of Hurst exponent indicated that indoor particulates showed higher persistence in the indoor environment compared to ambient xvii environment. Higher Hurst exponent values indicated that predictability of particulates is higher in indoor environment, which may be attributed to the controlled metrological and environment conditions in the indoor. The largest Lyapunov exponent (LLE) was used to estimate magnitude of chaos among particulates. The positive value of LLE indicated that time series concentrations of particulates exhibit chaotic behaviour in both indoor and outdoor environment. The complexity of particulate matter time series data was quantified using permutation entropy analysis. The finding indicated time series data of indoor particulates exhibited dynamically complex patterns compared to ambient particulate matter time series data. The higher complexity of indoor particulates depicted that controlling mechanism is not perturbed by external influences. In the ambient environment various metrological factors and traffic congestion may perturb the controlling mechanism which resulted in the loss of complexity. The temporal variations explored using sensitivity analysis of Poincare plot descriptors (SD1, SD2 and CCM) revealed that CCM is more robust measure to study the temporal variations of particulates in the indoor and outdoor environment. To predict the mass concentration of particulates, linear and radial support vector regressors and random forest approaches were used. The data of consecutive ten days was used to build the prediction model, which was later on used to predict mass concentration of six consecutive hours of next day. The finding indicated that random forest approach provided better prediction with least root mean squared error (RMSE) compared to other linear and radial support vector regressors.