pandas replace multiple values in column

import pandas as pd

df = pd.DataFrame([
	[4, -9, 8],
	[1, 2, -4],
    [2, 2, -8],
    [0, 7, -4],
	[2, 5, 1]],
	columns=['a', 'b', 'c'])

df = df.replace({'a':{1:11, 2:22}, 'b':{5:55, 2:22}})
print(df)

df['column name'] = df['column name'].replace(['1st old value','2nd old value',...],['1st new value','2nd new value',...])