The Agile Manifesto is a document that sets out the guiding principles for agile project management. It emphasizes the importance of individuals and interactions over processes and tools, working software over comprehensive documentation, customer collaboration over contract negotiation, and responding to change over following a plan. The manifesto was created by a group of 17 software developers in 2001 who were seeking more efficient ways of developing software. These principles are intended to create a more flexible and collaborative approach to work, which is highly valued in the agile methodology.

Scrum is a framework within Agile that emphasizes teamwork, accountability, and iterative progress towards a well-defined goal. Projects are divided into units of work called 'sprints', which are time-boxed iterations that typically last 2-4 weeks. Key roles in Scrum include the Product Owner, who represents the customer's needs; the Scrum Master, who is a facilitary role, and the Development Team, who delivers the product. Daily stand-up meetings, or 'scrums', are held to review progress and plan the day's work.

Kanban is a visual system used in Agile project management as a way to manage work by balancing the volume of work with the team's capacity. Work items are visualized using cards on a kanban board, allowing team members to see the status of every piece of work at any time. The key principle behind Kanban is to work on one item at a time and move it to completion, maximizing flow and minimizing work in progress. It encourages transparency and helps in identifying bottlenecks in the process.

Lean is an Agile philosophy that focuses on minimizing waste in order to increase customer value. The Lean principles originated from the Toyota Production System and they include defining value from the customer's perspective, identifying the value stream, creating flow by making sure work in progress is always moving forward, establishing pull so that nothing is made ahead of time, and pursuing perfection through continuous improvement. Lean has a strong focus on efficiency, quality, and continuous improvement.

Extreme Programming (XP) is an Agile software development methodology that aims to improve software quality and responsiveness to changing customer requirements. XP introduces simplicity, communication, feedback, and courage into software development. Its practices include continuous integration, automated testing, pair programming, and small releases, all of which are intended to improve the quality of the final product and the efficiency of the development process.

In Agile Project Management, a user story is a tool used in Agile software development to capture a description of a software feature from an end-user perspective. The user story describes the type of user, what they want and why. It helps to create a simplified description of a requirement and generates discussions within the team. User stories help to create a customer centric approach to development, encouraging teams to think in the customer's benefit. They also provide a standard format that encourages uniformity in defining user requirements.

Backlog grooming, also referred to as backlog refinement or story time, is a recurring event for agile product development teams. The primary purpose of a backlog grooming session is to ensure the next few sprints worth of user stories in the product backlog are prepared for sprint planning. Regular grooming sessions also ensure that the most important items are always ready to be included in the next sprint. It involves teams reviewing user stories and ensuring they are appropriately prioritized, and broken down to manageable sizes.

Agile modeling (AM) is a methodology for modeling and documenting systems based on best practices. It is a collection of values and principles, that can be applied on a software development project to improve productivity and flexibility to manage change. AM assumes that you have some sort of modeling skills and need to improve them, and that modeling is an important part of building high-quality software.

Agile estimating and planning is a key component in managing work flows in Agile project management. Agile estimating techniques include the use of story points, versus traditional estimating methods of duration and cost. Teams assign story points relative to work complexity, the amount of work, and risk or uncertainty. Once these story points are compiled in the backlog, they give a more long-term view of product development.

In Agile project management, a sprint is a set period of time during which specific work has to be completed and made ready for review. Each sprint begins with a planning meeting where the team decides what to complete in the coming sprint. Once a sprint has been delivered, the product is tested and reviewed (during what’s called a sprint retrospective). The next sprint then begins. Sprints are considered to be the heart of Agile as it allows for quick, iterative feedback that can be used to build better products quickly.