A formal personal introduction is more structured than an informal one. Instead of simply stating your name and what you do for a living, think about how you can best convey your goals and positive qualities. A well written formal introduction can come in handy for public speeches, college applications or in group interview settings where you'll want to leave a memorable and lasting impression.
Start with the most important fact in any introduction: your name. Put this information in an easily understandable opening sentence along with your hometown, profession or year in school. For the purposes of keeping the introduction formal, don't use any ice breakers or jokes.
Explain briefly why you are introducing yourself. Chances are, you're presenting this to a group of strangers. This can be a quick sentence or two starting off with "I'm applying because..." or "I'm running for office because...". Details aren't necessary at this point.
Give details about your skills and level of experience. Since you are trying to earn the confidence and respect of your listeners, don't be modest. For example, detail some of the projects you've completed or how many years you have been in the industry. So long as you don't cross the line into bragging, this introduction is the appropriate place for highlighting your strengths.
Choose one issue, anecdote or value that explains why you're special without telling your whole life story -- this makes the introduction personal and memorable. This should be a brief anecdote that cab be read aloud in less than one minute.
Close with a final word that sums up your position or plan. It should be clear to your listeners or readers who you are and the goals you plan to achieve.
Note
Whenever possible, plan your introduction ahead of time and practice it until you feel comfortable. Rather than sounding rehearsed, it will actually come across with confidence and self-assurance. Also, time yourself to make sure it's not too long.