Cover letter

Hi there, would anybody be so kind and would help me with my cover letter? What´s wrong with it, im not sure about some phrases.Thx in advance.

Dear Sir or Madam,
I would like to express my interest in studying at the xxx xxxx next year as the international student. In the folllowing letter I will introduce myself and explain why I think that xxxxx is the right choice for me.
My name is xx xxx, I am 18 years old. I am currently studying at 4-year grammar-school in xxxx. My graduation is in May 2014. I would like to apply for xxxx
Please allow me to briefly introduce myself.
I am serious, independent, dynamic, organized and responsible. I like meeting new people and cultures too. In addition, for me the possibility of studying abroad was always a great dream which I want to fulfil. I was looking for some good universities abroad, but the fees were so high, that I gave up. Two years ago, when I found out that you can study in Denmark for free, I applied right away and now I feel like I already belong there.
I am interested in travelling, meeting new people and cultures. I have been working in Italy during the last three years in summer and saved some money for my life in Denmark. I have also a friend from my hometown who is studying in Aalborg 2nd semester which can be really helpful for me.
I also welcome opportunity to learn another one language.Study in native language would ease me understanding of this country and its inhabitants and help me to create closer relation with professors and students.
Denmark is a country which attracts me, due to its culture but also the mentality of people who live there. I have discussed with several students who have been studying there and all were delighted, and assure me they enriched themselves in both a personal and professional way.
Applying at xxxx would also give me the opportunity to spend a period in a beautiful and friendly town, in a country that attract me for it’s being so tolerant and open-minded, to come in touch with Danish culture and kindness, and to meet many other students from other European countries and know other ways of life.
I am confident that my experience in Denmark would be extremely exciting, fun, and valuable for both my studies and overall general development.

Thank you for considering my request. I look forward to your positive response.
Yours faithfully,

xxx xxx
In xxxx xxx, xx/xx/xxxx