In [16]: df = pd.DataFrame(np.random.randn(3, 8), index=['A', 'B', 'C'], columns=index)

In [17]: df
Out[17]: 
first  bar     baz     foo     qux second  one  two  one  two  one  two  one 
A  0.895717 0.805244 -1.206412 2.565646 1.431256 1.340309 -1.170299 
B  0.410835 0.813850 0.132003 -0.827317 -0.076467 -1.187678 1.130127 
C  -1.413681 1.607920 1.024180 0.569605 0.875906 -2.211372 0.974466 

first    
second  two 
A  -0.226169 
B  -1.436737 
C  -2.006747 

In [23]: index.get_level_values(0)
Out[23]: Index(['bar', 'bar', 'baz', 'baz', 'foo', 'foo', 'qux', 'qux'], dtype='object', name='first')

In [24]: index.get_level_values('second')
Out[24]: Index(['one', 'two', 'one', 'two', 'one', 'two', 'one', 'two'], dtype='object', name='second')

In [25]: df['bar']
Out[25]: 
second  one  two
A  0.895717 0.805244
B  0.410835 0.813850
C  -1.413681 1.607920

In [26]: df['bar', 'one']
Out[26]: 
A 0.895717
B 0.410835
C -1.413681
Name: (bar, one), dtype: float64

In [27]: df['bar']['one']
Out[27]: 
A 0.895717
B 0.410835
C -1.413681
Name: one, dtype: float64

In [11]: s = pd.Series(np.random.randn(8), index=arrays)

In [12]: s
Out[12]: 
bar one -0.861849
  two -2.104569
baz one -0.494929
  two 1.071804
foo one 0.721555
  two -0.706771
qux one -1.039575
  two 0.271860
dtype: float64

In [34]: s + s[:-2]
Out[34]: 
bar one -1.723698
  two -4.209138
baz one -0.989859
  two 2.143608
foo one 1.443110
  two -1.413542
qux one   NaN
  two   NaN
dtype: float64

In [35]: s + s[::2]
Out[35]: 
bar one -1.723698
  two   NaN
baz one -0.989859
  two   NaN
foo one 1.443110
  two   NaN
qux one -2.079150
  two   NaN
dtype: float64