Can a Landlord increase the rent? If so, what are the laws pertaining to it. Thank you.

Of course they can given written notice or contractual term.

If you have a written lease that sets forth the amount for rent, then the Landlord cannot increase the rent until the end of the Lease term. If you don't have a written lease then the Landlord, in most locations, can increase the rent every pay period, with one pay period of notice before the increase takes effect.

Not only that, but some leases can have a clause built in to them that allows for increases within the term (usually a year) if heat is included in the rent.
On the other hand, some locales (mostly cities, not states) can have limits on what % an increase can be over the last year.

Please tell us more about your lease or terms if you need more answers.

Laws vary, where do you live? The answer is YES but how and when will vary depending on location

In the US, rent can be increased without a lease normally with a 30 day notice. With a lease it can only be changed, within the terms of the lease, or when the lease expires.

they may increase the rent, to basically any sum they want, (some areas state market value) Details as to where you live, how much is being paid now, what the increase is, you are talking about, would be helpful