What's this Japanese kanji style called and how to learn to write it? (link attached)?

Question:

The first pic from the top: http://research.ua.edu/2007/05/a-song-fr…

Answer:

Yes, it is the gyoshotai or 'semi-cursive' style. It is the style that people generally use when writing. If you study Japanese calligraphy, that will be included together with kaisho (regular), sosho (cursive) and kana

If you are interested there is an online calligraphy dictionary which show all three styles for each character.
http://www013.upp.so-net.ne.jp/santai/sa…
For further information: http://en.wikipedia.org/wiki/Japanese_ca…