You are looking for the .lower() method:

string1 = "hi"
string2 = "HI"
if string1.lower() == string2.lower():
    print("Equals!")
else:
    print("Different!")

Btw, There's another post here. Try looking at this.

Comparing strings in a case insensitive way seems trivial, but it's not. I will be using Python 3, since Python 2 is underdeveloped here.

The first thing to note is that case-removing conversions in Unicode aren't trivial. There is text for which text.lower() != text.upper().lower(), such as "ß":

>>> "ß".lower()
'ß'
>>> "ß".upper().lower()
'ss'

But let's say you wanted to caselessly compare "BUSSE" and "Buße". Heck, you probably also want to compare "BUSSE" and "BUẞE" equal - that's the newer capital form. The recommended way is to use casefold:

str.casefold()

Return a casefolded copy of the string. Casefolded strings may be used for caseless matching.

Casefolding is similar to lowercasing but more aggressive because it is intended to remove all case distinctions in a string. [...]

Do not just use lower. If casefold is not available, doing .upper().lower() helps (but only somewhat).

Then you should consider accents. If your font renderer is good, you probably think "ê" == "ê" - but it doesn't:

>>> "ê" == "ê"
False

This is because the accent on the latter is a combining character.

>>> import unicodedata
>>> [unicodedata.name(char) for char in "ê"]
['LATIN SMALL LETTER E WITH CIRCUMFLEX']
>>> [unicodedata.name(char) for char in "ê"]
['LATIN SMALL LETTER E', 'COMBINING CIRCUMFLEX ACCENT']

The simplest way to deal with this is unicodedata.normalize. You probably want to use NFKD normalization, but feel free to check the documentation. Then one does

>>> unicodedata.normalize("NFKD", "ê") == unicodedata.normalize("NFKD", "ê")
True

To finish up, here this is expressed in functions:

import unicodedata

def normalize_caseless(text):
    return unicodedata.normalize("NFKD", text.casefold())

def caseless_equal(left, right):
    return normalize_caseless(left) == normalize_caseless(right)