ssairam96,
"be" as a linking verb (also called a copula) connects a sentence subject with a noun, adjective, or adverb:
She is a doctor.
She is intelligent.
She is outside.
The other English linking verbs, with various functions, are: appear; become; feel; get; go; grow; look; prove; seem; smell; sound; taste; turn.
The verb be [is] of your "the baby is sleeping" is the auxiliary verb for the present progressive aspect, and "sleeping" is the present progressive participle of the verb "sleep."
"be" is the passive auxiliary: "The thief was captured in Toronto."
"be" also is a full intransitive verb meaning "to have being; exist": "there is something wrong";
or "to take place;happen": "there's been an accident."
"be" acts as its own auxiliary in that it can carry the negtive particle, and invert with the sentence subject in a question: "he's not here"; is "she coming?"
And "be" has eight forms: be; being; been; am; is; are; was; were. It's the hardest word to deal with in the English language, so don't be discouraged. You may not be able to talk about it comfortably, but you use it very well.