Depending on research you might find many agile methodologies. Below list of the most common ones:
Scrum is a lightweight framework for managing product development. It is characterized by its iterative and incremental approach, where work is broken down into short sprints with frequent reviews and feedback. Scrum is a good choice for projects that need to be delivered quickly and adapt to changing requirements.
Kanban is a more flexible and adaptable agile methodology than Scrum. It is based on a visual board that shows the workflow of work items, and it allows teams to pull work in from the backlog as they have capacity to do so. Kanban is a good choice for projects with complex or uncertain requirements, or for teams that need to be able to respond to changing priorities.
Extreme Programming (XP) is a set of practices for software development that focus on producing high-quality software quickly and efficiently. XP practices include pair programming, test-driven development, and continuous integration. XP is a good choice for projects that require a high level of quality and predictability.
Lean Software Development is a methodology that emphasizes eliminating waste and delivering value to customers quickly and efficiently. It is inspired by the Toyota Production System and is closely related to Agile methodologies.
Crystal is a family of agile methodologies that are based on the concept of tailoring the methodology to the specific needs of the project and the team. There are several different Crystal methodologies, each with its own level of formality. Crystal is a good choice for projects that require a high level of customization.
Dynamic Systems Development Method (DSDM) is an agile methodology that is based on the principles of timeboxing, collaboration, and focus on business needs. DSDM is a good choice for projects that require a high level of flexibility and adaptability.
Feature-Driven Development (FDD) is an agile methodology that is based on the concept of breaking down a project into features. FDD is a good choice for projects that require a high level of clarity and structure.
Scrumban combines the iterative and incremental approach of Scrum with the flexibility of Kanban.
SAF - Scaled Agile Framework (SAFe), a set of organizational and workflow patterns for implementing agile practices at an enterprise scale. It is a widely adopted framework that helps large organizations manage complex software development projects by providing a structured approach to planning, collaborating, and delivering value.
Prince2Agile is a hybrid project management approach that combines the strengths of two well-established methodologies: PRINCE2 (Projects IN Controlled Environments) and Agile methodologies like Scrum or Kanban. It aims to address the limitations of traditional project management methods, which often lack flexibility and responsiveness, while also providing the structure and governance needed for complex projects.