How can I combine many dataframes in python?

it seems, that level_0 could be your index, right?

you have:

>>> level0 = ['ALL','AWA','REM','S1','S2','SWS']
>>> df1 = pd.DataFrame(data={'level_0':level0, 'col1':np.random.randint(0,9,6)})
>>> df2 = pd.DataFrame(data={'level_0':level0, 'col2':np.random.randint(0,9,6)})
>>> df3 = pd.DataFrame(data={'level_0':level0, 'col3':np.random.randint(0,9,6)})

>>> df1
   col1 level_0
0     5     ALL
1     8     AWA
2     5     REM
3     3      S1
4     8      S2
5     4     SWS

>>> df2
   col2 level_0
0     4     ALL
1     1     AWA
2     3     REM
3     2      S1
4     5      S2
5     1     SWS

>>> df3
   col3 level_0
0     1     ALL
1     3     AWA
2     0     REM
3     4      S1
4     2      S2
5     3     SWS

>>> pd.concat([df1,df2,df3], axis=1)

   col1 level_0  col2 level_0  col3 level_0
0     5     ALL     4     ALL     1     ALL
1     8     AWA     1     AWA     3     AWA
2     5     REM     3     REM     0     REM
3     3      S1     2      S1     4      S1
4     8      S2     5      S2     2      S2
5     4     SWS     1     SWS     3     SWS

you can set level_0 as your index, then concatenate:

>>> pd.concat([df1.set_index('level_0'), df2.set_index('level_0'), df3.set_index('level_0')], axis=1)

         col1  col2  col3
level_0                  
ALL         5     4     1
AWA         8     1     3
REM         5     3     0
S1          3     2     4
S2          8     5     2
SWS         4     1     3

of if it's not an index, you can remove it before concat:

>>> pd.concat([df1.drop('level_0', axis=1), df2.drop('level_0', axis=1), df3.drop('level_0', axis=1)], axis=1)

   col1  col2  col3
0     5     4     1
1     8     1     3
2     5     3     0
3     3     2     4
4     8     5     2
5     4     1     3