hay=there is (present) hubo = there used to be (imperfect past) habrá = there will be (future) había =there was (perfect past) haya = (this is used in no real situation): quiero que haya paz (this is no real, because there isnt peace, it's hipothetical)

Haber is an auxiliary verb. Hay- there is/are Hubo- there was/were Habrá- there will be Había- there was/were (imperfect tense) Haya- there is/are (subjunctive tense) Hope this helps you.

I'll throw in some example sentences to help flesh it out a bit Hay = there is/are Hay un gato = There is a cat Hay tres tazas = There are three cups Hubo = past tense version of "there is", one time occurrence Hubo un accidente = There was an accident Habrá = future tense version of "there is" Habrá música y luz = There will be music & light Había = past tense version of "there is", recurring occurrence Había muchos accidentes en ese barrio = There were many accidents in that neighborhood. Haya = I'm not really familiar with this one, I'll defer to the other guys on this. Also, these are just some usages of the verb Haber. The verb is commonly used as "to have done something" Yo he comido = I HAVE eaten Nosotros hemos comido = We HAVE eaten Usted ha estado aquí por tres meses = You HAVE been here for three months Ella nunca había comido pollo frito, antes de la semana pasada = She HAD never eaten fried chicken, before last week Él habrá visitado China = He WILL HAVE visited China Tú habrías ido = You WOULD HAVE gone