Adjusting how much text can be seen in a post by formatting

Still new to Word Press; second forum post. I am using Twenty Eleven as my theme and I’m placing content on pages in my blog. When I’m editing a post, it says in one place “Format” and various options are given like Standard, Aside, Link, etc. In the “Standard” format, the whole post is shown from beginning to the end. The only one I found that would shorten the amount of text that can initially be seen on the site is the “Gallery” option and this cuts the visual text down to about two lines. You have to click to see the rest of the post.
What I would like to have is a way to not show the whole post, but to have more showing than just the first two lines. Like the first paragraph could show or some way that I can control or adjust this so that more text would show, but not all. Could anyone help me with this? Thanks so much. Mark