Parameter-Efficient Fine-Tuning (PEFT) methods offer a cost-effective approach to adapt large language models (LLMs) by optimizing memory and computational performance without the need to train all parameters. These methods are categorized into additive, selective, and reparameterization-based approaches, each with unique techniques for parameter adjustment. Additive methods introduce new parameters to the model, such as adapters and soft prompts, to facilitate task-specific adaptation while maintaining memory efficiency. Selective methods focus on training a fraction of existing parameters, though they may become computationally intensive. Reparameterization-based techniques, such as Low-Rank Adaptation (LoRA), leverage low-rank representations to decrease trainable parameters, enhancing storage and training efficiency. PEFT methods are further advanced by innovations like Quantized Low-Rank Adaptation (QLoRA) and Principal Singular Values and Singular Vectors Adaptation (PiSSA), which improve fine-tuning accuracy and resource use. These methods enable efficient adaptation of LLMs, making them accessible for various applications, from language understanding to complex scientific tasks, while conserving computational resources and maintaining high performance.