pandas: merge (join) two data frames on multiple columns

Try this

new_df = pd.merge(A_df, B_df,  how='left', left_on=['A_c1','c2'], right_on = ['B_c1','c2'])

https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.DataFrame.merge.html

left_on : label or list, or array-like Field names to join on in left DataFrame. Can be a vector or list of vectors of the length of the DataFrame to use a particular vector as the join key instead of columns

right_on : label or list, or array-like Field names to join on in right DataFrame or vector/list of vectors per left_on docs

the problem here is that by using the apostrophes you are setting the value being passed to be a string, when in fact, as @Shijo stated from the documentation, the function is expecting a label or list, but not a string! If the list contains each of the name of the columns beings passed for both the left and right dataframe, then each column-name must individually be within apostrophes. With what has been stated, we can understand why this is inccorect:

new_df = pd.merge(A_df, B_df,  how='left', left_on='[A_c1,c2]', right_on = '[B_c1,c2]')

And this is the correct way of using the function:

new_df = pd.merge(A_df, B_df,  how='left', left_on=['A_c1','c2'], right_on = ['B_c1','c2'])

Another way of doing this:

new_df = A_df.merge(B_df, left_on=['A_c1','c2'], right_on = ['B_c1','c2'], how='left')

you can use below which is short and simple to understand:

merged_data= df1.merge(df2, on=["column1","column2"])