https://resources.environment.yale.edu/content/documents/00001033/Sample-Project-Manager-Cover-Letter.pdf 

Dear Ms. EMPLOYER,
I am writing to apply for the IT Project Manager vacancy which I saw posted on LinkedIn. I am interested in engaging with a company in its growth phase and contributing to the coordination of complex research-oriented IT projects. I am confident that my experience managing software development and data-driven research projects, as well as my strong independent initiative and analytical skills, make me an ideal candidate for the position.
This spring I am completing an MSc in Information Technology Project Management at the Budapest University of Technology and Economics, where I focused on agile methodologies, stakeholder management, and technical project delivery. My master’s studies and professional experience have given me a comprehensive understanding of IT project management processes, software development lifecycles, and research-supporting data infrastructures. Based on my work at the Centre for Social Sciences of the Hungarian Academy of Sciences, I have extensive experience coordinating interdisciplinary teams and supporting research projects with custom technical solutions. I am fluent in Hungarian and English, have strong written communication skills, excellent problem-solving abilities, and the ability to work collectively with diverse stakeholders.
At the Centre for Social Sciences of the Hungarian Academy of Sciences in Budapest, I was responsible for coordinating multiple concurrent research IT projects with international partners. This gave me first-hand exposure to the full project lifecycle, particularly the planning, implementation, and delivery phases of research-focused IT systems. Specifically, I gained experience managing custom data processing pipelines, coordinating developers and researchers across countries, and implementing project tracking tools such as Jira and Confluence. Among my duties supporting project coordination activities, I also facilitated collaboration with external vendors, maintained project documentation, and supported project-related workshops and internal trainings.
Building on my experience in academic research environments, I previously worked as a Junior Project Manager at a web development company, where I managed the end-to-end delivery of web-based projects for corporate and NGO clients. I coordinated cross-functional teams using Scrum methodology and ensured projects were delivered within agreed timelines and budgets. Earlier in my career, I also supported large-scale IT projects as an IT Analyst in the telecommunications sector, gaining a solid technical foundation and experience with quality assurance and requirements analysis.
I believe I would bring valuable expertise and experience to your team and would be happy to discuss potential positions and my qualifications further.
Thank you for your time and consideration, I look forward to hearing from you.
Sincerely, Márton László Kovács