After reading your essay you probably saw that you had made some grammar mistakes.

Ooops -- see that error? I made a #12 error.

The introductory element is usually a word or phrase that precedes the main independent clause (the main sentence); this word or phrase needs to be followed by a comma so readers can clearly identify the main sentence. In my sentence, the comma should appear here:

After reading your essay, you probably saw that you had made some grammar mistakes.

For comma errors, start with a quick review of comma rules with The Punctuation Guide.
Introductory words/phrases/clauses can be really confusing; don't get stuck with the explanations of these terms unless you're really interested. What's more important is that you learn the concept. Purdue's Online Writing Lab provides good examples here.

The following information comes from the website "Writer's Relief." I post it here to avoid the dozens of pop-up ads on the website itself, but you can find the original source at: http://writersrelief.com/blog/2008/06/how-to-use-commas-after-introductory-phrases/

Using commas after introductory phrases or other words. When you’re considering whether or not to put a comma after a word in the beginning of a sentence, there are a few rules to keep in mind. Commas exist to indicate a natural pause in a sentence and to avoid sentence confusion. In many cases it is the writer’s choice whether or not to use a comma. Here are a few guidelines to follow.

DO use a comma:

–After introductory exclamatories and after expressions of affirmation or negation.

Well, it’s about time. Oh, you shouldn’t have! Yes, I’d love to.

–After an introductory clause.

As I told you, the principal won’t be back until Monday.

–After an introductory prepositional phrase of more than four words.

After driving for more than eight fun-filled hours, we finally arrived at the motel.

–After an introductory verbal phrase, appositive phrase, or absolute phrase.

Having formed an instant bond, the boy and the puppy quickly became inseparable.

In order to give a good estimate, the plumber spent over an hour investigating the leaky pipes.

A lawyer from Texas, John Stetson is an expert in copyright law.

–After introductory transitional words.

However, I never said I would actually attend the party.

Of course, I wasn’t actually invited…

Do not use a comma when a gerund or an infinitive is used as a subject.

Watering the lawn is a good way to attract birds.

To tackle the subject without any research would be foolish.