The key points from this module are:
Digital Signature is a valid signature on a message, received by a receiver, which guarantees the authenticity and integrity of the message. 
 
Applications of Digital Signatures include:


Digital certificates and Public-Key Infrastructures(PKI)
Software updates
Contract signing, i.e legal applications

Comparison between Digital Signatures and Message Authentication Code(MAC) Include:

In digital signatures, key-agreement is not a challenge. For MAC, key-agreement is very challenging.
Digital Signatures are Publicly verifiable and transferable; for MAC, it is not Publicly verifiable or transferable.
Digital Signatures provides non-repudiation. MAC provides no non-repudiation.
Digital Signatures are computationally slow, while MAC is computationally very fast.

Schnorr Identification Scheme is based on the idea that a Prover authenticates itself by proving that it knows the Discrete Log of a Publicly known value y, in a Zero-Knowledge fashion; a Verifier challenges the Prover by demanding a random linear combination of the Discrete Log of y.
The Fiat-Shamir transformation is a 3-round interactive Identification Scheme which has the structure of commitment, challenge and response. The transformation converts an Interactive Protocol into a Non-Interactive Protocol; In other words, if you have an Identification Scheme and want to get a Signature Scheme, to sign a message, the Signer acts as a Prover and runs the whole Identification Prototcol itself.
The Fiat-Shamir transformation is a 3-round interactive Identification Scheme which has the structure of commitment, challenge and response. The transformation converts an Interactive Protocol into a Non-Interactive Protocol; In other words, if you have an Identification Scheme and want to get a Signature Scheme, to sign a message, the Signer acts as a Prover and runs the whole Identification Protocol itself.