The core principles of agile methodology in software development include iterations, collaboration, flexibility, and customer feedback. Agile emphasizes delivering functional software in short cycles, known as sprints, allowing for continuous improvement and adaptation to changes. Involving stakeholders and teams in regular communication fosters collaboration and transparency, leading to better-aligned products with customer needs. The Agile Manifesto also highlights the importance of valuing individuals and interactions over processes and tools, and working software over comprehensive documentation. These principles collectively enhance responsiveness to change and increase the overall effectiveness of the development process.