Correct spelling, explanation: the word originates in Old French, when the form agreer used to mean make agreeable to. In the form that we know it today the word appeared in late Middle English. Other common forms that come from the family of this word include: agree, disagree, and disagreement.

Expressions with agreement:
You can reach an agreement, come to an agreement, and enter into agreement. When it comes to prepositions you can have an agreement with someone or have an agreement on something. Some typical collocations with the word include a formal agreement, a written agreement, a legal agreement, written or unwritten agreement.

Definition of agreement:
1. noun – a state when two or more people have the same opinion on something,
We reached an agreement that it’s high time to get the work done.
2. noun – a formal arrangement between two parties,
After long negotiations, the two companies finally reached an agreement.
3. noun – in grammar, when two words have the same form,
There should always be an agreement between the subject and a verb in a sentence.

Incorrect spelling, explanation: often, when there is a double letter in a word, users tend to forget which one should be doubled. A similar case happens with the word agreement and as a result, a common mistake is the form aggreement, which, naturally, is wrong.