Worked For 3 Months and Terminated Without A Contract

Hello, I am an American in Al Khobar in the Eastern Province of Saudi Arabia. I have an iqama that specifies that I am an English instructor.
  Recently, I received a job offer for a company to work in Al Khobar. I started work in January, and I thought that I was fulfilling my job duties. However, the employer suddenly told me I wasn't needed and fired me.
  My job offer did not contain any words about probation period, notice of termination, or anything specific. I carried out my assignments to the best of my ability and a positive attitude. I received only good feedback about my work performance. On Thursday (March 28), the company terminated my employment. Their reasoning was that students were not attending classes, therefore I was at fault. I believe I should have received a contract with mutual conditions for employment, before they ended my job. I think I am correct in my view.
  I talked with a legal adviser, and he told me that the company acted illegally in employing me without a contract, and they are also required to pay out the remainder (9 months) of the agreed employment period stated in the job offer.
Did the company act illegally? What is the penalty for that?
Are they required to pay out the remainder of the employment period?

Making you work without giving you a copy of the contract means the company is being sneaky and hiding something which they don't want you to know. This means it's illegal.

During 3 months it's their right to end your contract as in Saudi three months probation period is something in which they can hire you or fire you depending on their mood. I don't think you're to blame for the students or anything as they can use any excuse to let you go.
I recommend contact the ministry of labor hotline number and getting the copy of the work contract before doing anything. Otherwise you have no proof.

Thank you, Justaman. The company never gave me a contract to sign, so there is no "hidden" copy of a contract. When I asked the program manager why I never received a contract to sign, before he fired me, he said the company didn't like to do this.
I like your suggestion. I will contact the Ministry of Labour Office today.
Kind Regards,
Jacques

All the best. Be firm and don't sign any Arabic document unless you know what's it about.