This lecture covers the fundamentals of language models, focusing on fixed-context neural models and recurrent neural networks (RNNs). It begins with an introduction to language models, discussing the limitations of n-gram models, particularly their inability to capture similarities between sequences unless they overlap. The instructor explains how neural networks can address these issues by composing word embeddings into vectors for natural language processing. The lecture then delves into fixed-context neural language models, illustrating how they predict the next word based on a given context. The discussion highlights the advantages of these models, such as overcoming sparsity problems and reducing model size. However, it also addresses their limitations, including the challenge of encoding long-range dependencies. The lecture transitions to recurrent neural networks, explaining their structure and how they maintain a feedback loop to model variable-length sequences. The instructor emphasizes the importance of RNNs in capturing the history of sequences, making them suitable for various natural language tasks.