diff --git a/tools_numpy.ipynb b/tools_numpy.ipynb
index 4743592..9a27cd8 100644
--- a/tools_numpy.ipynb
+++ b/tools_numpy.ipynb
@@ -84,7 +84,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "It's just as easy to create a 2D array (ie. a matrix) by providing a tuple with the desired number of rows and columns. For example, here's a 3x4 matrix:"
+    "It's just as easy to create a 2D array (i.e. a matrix) by providing a tuple with the desired number of rows and columns. For example, here's a 3x4 matrix:"
    ]
   },
   {
@@ -122,7 +122,7 @@
     "* An array's list of axis lengths is called the **shape** of the array.\n",
     "    * For example, the above matrix's shape is `(3, 4)`.\n",
     "    * The rank is equal to the shape's length.\n",
-    "* The **size** of an array is the total number of elements, which is the product of all axis lengths (eg. 3*4=12)"
+    "* The **size** of an array is the total number of elements, which is the product of all axis lengths (e.g. 3*4=12)"
    ]
   },
   {
@@ -275,7 +275,7 @@
    "metadata": {},
    "source": [
     "## `np.ones`\n",
-    "Many other NumPy functions create `ndarrays`.\n",
+    "Many other NumPy functions create `ndarray`s.\n",
     "\n",
     "Here's a 3x4 matrix full of ones:"
    ]
@@ -368,7 +368,7 @@
    "metadata": {},
    "source": [
     "## np.array\n",
-    "Of course you can initialize an `ndarray` using a regular python array. Just call the `array` function:"
+    "Of course, you can initialize an `ndarray` using a regular python array. Just call the `array` function:"
    ]
   },
   {
@@ -453,7 +453,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Of course you can provide a step parameter:"
+    "Of course, you can provide a step parameter:"
    ]
   },
   {
@@ -480,7 +480,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "However, when dealing with floats, the exact number of elements in the array is not always predictible. For example, consider this:"
+    "However, when dealing with floats, the exact number of elements in the array is not always predictable. For example, consider this:"
    ]
   },
   {
@@ -679,7 +679,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "NumPy first creates three `ndarrays` (one per dimension), each of shape `(3, 2, 10)`. Each array has values equal to the coordinate along a specific axis. For example, all elements in the `z` array are equal to their z-coordinate:\n",
+    "NumPy first creates three `ndarray`s (one per dimension), each of shape `(3, 2, 10)`. Each array has values equal to the coordinate along a specific axis. For example, all elements in the `z` array are equal to their z-coordinate:\n",
     "\n",
     "    [[[ 0.  0.  0.  0.  0.  0.  0.  0.  0.  0.]\n",
     "      [ 0.  0.  0.  0.  0.  0.  0.  0.  0.  0.]]\n",
@@ -770,7 +770,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Available data types include `int8`, `int16`, `int32`, `int64`, `uint8`|`16`|`32`|`64`, `float16`|`32`|`64` and `complex64`|`128`. Check out [the documentation](http://docs.scipy.org/doc/numpy-1.10.1/user/basics.types.html) for the full list.\n",
+    "Available data types include signed `int8`, `int16`, `int32`, `int64`, unsigned `uint8`|`16`|`32`|`64`, `float16`|`32`|`64` and `complex64`|`128`. Check out the documentation for the [basic types](https://numpy.org/doc/stable/user/basics.types.html) and [sized aliases](https://numpy.org/doc/stable/reference/arrays.scalars.html#sized-aliases) for the full list.\n",
     "\n",
     "## `itemsize`\n",
     "The `itemsize` attribute returns the size (in bytes) of each item:"
@@ -850,7 +850,7 @@
     }
    ],
    "source": [
-    "if (hasattr(f.data, \"tobytes\")):\n",
+    "if hasattr(f.data, \"tobytes\"):\n",
     "    data_bytes = f.data.tobytes() # python 3\n",
     "else:\n",
     "    data_bytes = memoryview(f.data).tobytes() # python 2\n",
@@ -862,7 +862,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Several `ndarrays` can share the same data buffer, meaning that modifying one will also modify the others. We will see an example in a minute."
+    "Several `ndarray`s can share the same data buffer, meaning that modifying one will also modify the others. We will see an example in a minute."
    ]
   },
   {
@@ -1333,7 +1333,7 @@
    "metadata": {},
    "source": [
     "Broadcasting rules are used in many NumPy operations, not just arithmetic operations, as we will see below.\n",
-    "For more details about broadcasting, check out [the documentation](https://docs.scipy.org/doc/numpy-dev/user/basics.broadcasting.html)."
+    "For more details about broadcasting, check out [the documentation](https://numpy.org/doc/stable/user/basics.broadcasting.html)."
    ]
   },
   {
@@ -1384,7 +1384,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Note that `int16` is required to represent all *possible* `int8` and `uint8` values (from -128 to 255), even though in this case a uint8 would have sufficed."
+    "Note that `int16` is required to represent all *possible* `int8` and `uint8` values (from -128 to 255), even though in this case a `uint8` would have sufficed."
    ]
   },
   {
@@ -2258,15 +2258,15 @@
    ],
    "source": [
     "a[3] = 4000\n",
-    "another_slice  # similary, modifying the original array does not affect the slice copy"
+    "another_slice  # similarly, modifying the original array does not affect the slice copy"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## Multi-dimensional arrays\n",
-    "Multi-dimensional arrays can be accessed in a similar way by providing an index or slice for each axis, separated by commas:"
+    "## Multidimensional arrays\n",
+    "Multidimensional arrays can be accessed in a similar way by providing an index or slice for each axis, separated by commas:"
    ]
   },
   {
@@ -3119,7 +3119,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "This was possible because q1, q2 and q3 all have the same shape (except for the vertical axis, but that's ok since we are stacking on that axis).\n",
+    "It was possible because q1, q2 and q3 all have the same shape (except for the vertical axis, but that's ok since we are stacking on that axis).\n",
     "\n",
     "## `hstack`\n",
     "We can also stack arrays horizontally using `hstack`:"
@@ -3172,7 +3172,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "This is possible because q1 and q3 both have 3 rows. But since q2 has 4 rows, it cannot be stacked horizontally with q1 and q3:"
+    "It is possible because q1 and q3 both have 3 rows. But since q2 has 4 rows, it cannot be stacked horizontally with q1 and q3:"
    ]
   },
   {
@@ -3691,7 +3691,7 @@
    "metadata": {},
    "source": [
     "# Linear algebra\n",
-    "NumPy 2D arrays can be used to represent matrices efficiently in python. We will just quickly go through some of the main matrix operations available. For more details about Linear Algebra, vectors and matrics, go through the [Linear Algebra tutorial](math_linear_algebra.ipynb).\n",
+    "NumPy 2D arrays can be used to represent matrices efficiently in python. We will just quickly go through some of the main matrix operations available. For more details about Linear Algebra, vectors and matrices, go through the [Linear Algebra tutorial](math_linear_algebra.ipynb).\n",
     "\n",
     "## Matrix transpose\n",
     "The `T` attribute is equivalent to calling `transpose()` when the rank is ≥2:"
@@ -3927,7 +3927,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "**Caution**: as mentionned previously, `n1*n2` is *not* a matric multiplication, it is an elementwise product (also called a [Hadamard product](https://en.wikipedia.org/wiki/Hadamard_product_(matrices)))."
+    "**Caution**: as mentioned previously, `n1*n2` is *not* a matrix multiplication, it is an elementwise product (also called a [Hadamard product](https://en.wikipedia.org/wiki/Hadamard_product_(matrices)))."
    ]
   },
   {
@@ -4019,7 +4019,7 @@
    "metadata": {},
    "source": [
     "## Identity matrix\n",
-    "The product of a matrix by its inverse returns the identiy matrix (with small floating point errors):"
+    "The product of a matrix by its inverse returns the identity matrix (with small floating point errors):"
    ]
   },
   {
@@ -4048,7 +4048,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "You can create an identity matrix of size NxN by calling `eye`:"
+    "You can create an identity matrix of size NxN by calling `eye(N)` function:"
    ]
   },
   {
@@ -4637,7 +4637,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "As you can see, both `X` and `Y` are 768x1024 arrays, and all values in `X` correspond to the horizontal coordinate, while all values in `Y` correspond to the the vertical coordinate.\n",
+    "As you can see, both `X` and `Y` are 768x1024 arrays, and all values in `X` correspond to the horizontal coordinate, while all values in `Y` correspond to the vertical coordinate.\n",
     "\n",
     "Now we can simply compute the result using array operations:"
    ]
@@ -4678,7 +4678,6 @@
    ],
    "source": [
     "import matplotlib.pyplot as plt\n",
-    "import matplotlib.cm as cm\n",
     "\n",
     "fig = plt.figure(1, figsize=(7, 6))\n",
     "plt.imshow(data, cmap=\"hot\")\n",
@@ -4733,7 +4732,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Done! Since the file name contains no file extension was provided, NumPy automatically added `.npy`. Let's take a peek at the file content:"
+    "Done! Since the file name contains no file extension, NumPy automatically added `.npy`. Let's take a peek at the file content:"
    ]
   },
   {
@@ -5031,8 +5030,8 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "# What next?\n",
-    "Now you know all the fundamentals of NumPy, but there are many more options available. The best way to learn more is to experiment with NumPy, and go through the excellent [reference documentation](http://docs.scipy.org/doc/numpy/reference/index.html) to find more functions and features you may be interested in."
+    "# What's next?\n",
+    "Now you know all the fundamentals of NumPy, but there are many more options available. The best way to learn more is to experiment with NumPy, and go through the excellent [reference documentation](https://numpy.org/doc/stable/reference/index.html) to find more functions and features you may be interested in."
    ]
   }
  ],