Time series data, defined by equally spaced points over time, is essential in fields like medicine, telecommunications, and energy. Analyzing it involves tasks such as classification, clustering, prototyping, and regression. Classification identifies normal vs. abnormal movements in skeleton-based motion sequences, clustering detects stock market behavior patterns, prototyping expands physical therapy datasets, and regression predicts patient recovery. Deep learning has recently gained traction in time series analysis due to its success in other domains. This thesis leverages deep learning to enhance classification with feature engineering, introduce foundation models, and develop a compact yet state-of-the-art architecture. We also address limited labeled data with self-supervised learning. Our contributions apply to real-world tasks, including human motion analysis for action recognition and rehabilitation. We introduce a generative model for human motion data, valuable for cinematic production and gaming. For prototyping, we propose a shape-based synthetic sample generation method to support regression models when data is scarce. Lastly, we critically evaluate discriminative and generative models, identifying limitations in current methodologies and advocating for a robust, standardized evaluation framework. Our experiments on public datasets provide novel insights and methodologies, advancing time series analysis with practical applications.