In [1]: 
import numpy as np
In [2]: 
a = np.random.rand(3,4,5)
a.shape
Out[2]:
(3, 4, 5)

What's the result of this?

In [3]: 
a[0].shape
Out[3]:
(4, 5)

And this?

In [4]: 
a[...,2].shape
Out[4]:
(3, 4)
In [5]: 
a[1,0,3]
Out[5]:
0.025588609438720655

Like all other things in Python, numpy indexes from 0.

In [6]: 
a[3,2,2].shape

---------------------------------------------------------------------------
IndexError                                Traceback (most recent call last)
<ipython-input-6-4c22dfd164ed> in <module>()
      1 #keep
----> 2 a[3,2,2].shape

IndexError: index 3 is out of bounds for axis 0 with size 3
In [7]: 
a[:,2].shape
Out[7]:
(3, 5)

Indexing into numpy arrays usually results in a so-called view.

In [8]: 
a = np.zeros((4,4))
a
Out[8]:
array([[ 0.,  0.,  0.,  0.],
       [ 0.,  0.,  0.,  0.],
       [ 0.,  0.,  0.,  0.],
       [ 0.,  0.,  0.,  0.]])

Let's call b the top-left $2\times 2$ submatrix.

In [9]: 
b = a[:2,:2]
b
Out[9]:
array([[ 0.,  0.],
       [ 0.,  0.]])

What happens if we change b?

In [10]: 
b[1,0] = 5
b
Out[10]:
array([[ 0.,  0.],
       [ 5.,  0.]])
In [12]: 
print(a)

[[ 0.  0.  0.  0.]
 [ 5.  0.  0.  0.]
 [ 0.  0.  0.  0.]
 [ 0.  0.  0.  0.]]

To decouple b from a, use .copy().

In [13]: 
b = b.copy()
b[1,1] = 7
print(a) 

[[ 0.  0.  0.  0.]
 [ 5.  0.  0.  0.]
 [ 0.  0.  0.  0.]
 [ 0.  0.  0.  0.]]

You can also index with other arrays:

In [14]: 
a = np.random.rand(4,4)
a
Out[14]:
array([[ 0.94747406,  0.89080192,  0.46799144,  0.54340544],
       [ 0.54409333,  0.27586608,  0.60682897,  0.61962813],
       [ 0.06203009,  0.7958913 ,  0.93468584,  0.88864481],
       [ 0.98627827,  0.73442815,  0.90304704,  0.18186312]])
In [15]: 
i = np.array([0,2])
a[i]
Out[15]:
array([[ 0.94747406,  0.89080192,  0.46799144,  0.54340544],
       [ 0.06203009,  0.7958913 ,  0.93468584,  0.88864481]])

And with conditionals:

In [16]: 
a>0.5
Out[16]:
array([[ True,  True, False,  True],
       [ True, False,  True,  True],
       [False,  True,  True,  True],
       [ True,  True,  True, False]], dtype=bool)
In [17]: 
a[a>0.5]
Out[17]:
array([ 0.94747406,  0.89080192,  0.54340544,  0.54409333,  0.60682897,
        0.61962813,  0.7958913 ,  0.93468584,  0.88864481,  0.98627827,
        0.73442815,  0.90304704])