Explain the theoretical framework and mathematical principles underlying quantum field theory, elucidating its role in modern particle physics and the study of fundamental interactions. Discuss the concept of quantized fields, their behavior, and the significance of symmetries in the formulation of quantum field theories. Analyze the renormalization procedure and its implications for addressing divergences in quantum field theories, highlighting its role in achieving meaningful predictions and reconciling theoretical frameworks with experimental observations in high$-$energy physics.