This paper provides a comprehensive overview of Large Language Models (LLMs), defining them as advanced deep learning algorithms characterised by their immense scale and ability to generate human-like text. It delves into their core characteristics, evolution as a type of generative AI, and their position within the broader AI and deep learning landscape. The foundational mechanics of LLMs are explored, including their reliance on deep learning and neural network principles, and a detailed examination of the pivotal Transformer architecture, encompassing its encoder-decoder framework, self-attention mechanism, positional encoding, and the role of embeddings and feedforward layers. The paper also outlines the training paradigms, from large-scale data collection and unsupervised pre-training to task-specific fine-tuning and the emergence of zero-shot and few-shot learning capabilities. Finally, it highlights the diverse functions and applications of LLMs in machine learning, covering core Natural Language Processing tasks like text generation, question answering, summarisation, translation, and sentiment analysis, as well as their broader impact across industries such as healthcare, customer service, R&D, and cybersecurity.