Congrats! You've received an offer of representation. Now it's time to review your agent agreement. Below are some tips to keep in mind:
This may seem obvious but look to see if the commission rates are standard (10% for domestic deals; 20% for foreign and 20-25-% for certain territories and certain subsidiary rights). Of course these rates should be split if the agent uses a co-agent for certain rights like translation and book-to-film adaptations.
Review if the agreement is for your entire career or for one book or a certain amount of books. Yes you want an agent to theoretically champion your books for your writing life, but perhaps your situation calls for representation of a single book or a few books.
Review whether your agent is your agent "coupled with interest." You should delete these words. It essentially means the agency relationship between you and your agent is irrevocable. In addition to be "coupled with interest" the agent has to have an interest in the subject matter of the agency itself, and not an interest in the results of the agency (i.e., the agent likely has to have an interest in the copyright of your book, not just the agent's commission that results from your book), so most agencies likely use the language incorrectly.
Review the termination provisions carefully about when you can terminate your contract and when and where your agent may be owed a commission when your relationship ends.
If you have any questions, contact me at 914-775-8774 or contact me on my homepage.