diff --git a/README.md b/README.md
index a48329c..d449020 100644
--- a/README.md
+++ b/README.md
@@ -14,7 +14,7 @@ step, you make some modules, i.e. separate python files, where you
 collect this code. These modules can be easily imported from other
 scripts in the very same directory.
 
-For example, consider a module `addition.py` and a script `anayze.py`
+For example, consider a module `addition.py` and a script `analyze.py`
 both in the same directory:
 ```txt
 ├── addition.py
@@ -38,7 +38,7 @@ y = add_two(x)
 
 This works, however, only if scripts and modules are in the same
 directory (or if modules are in sub-directories). To make modules
-available in other places of your file system or for even for other
+available in other places of your file system or even for other
 people, you need to turn the modules into packages.
 
 
@@ -46,12 +46,12 @@ people, you need to turn the modules into packages.
 
 First we make a project directory for our new package. Usually the
 name of the project directory is the same as the one of the
-package. Here, however, we called `packagehowto` and the name of the
-package is `numerix`.
+package. Here, however, we call the proejct directory `packagehowto`
+and the name of the package `numerix`.
 
 A package is a directory, and the name of the package is the name of
 this directory, here `numerix`. Inside the package directory we put
-all the modules, here `addition.py`.
+all the modules, for now just `addition.py`.
 
 What makes this directory a package is the presence of a file named
 `__init__.py`. This file is executed when the package is imported. For
@@ -68,7 +68,7 @@ packagehowto/
 ```
 
 A package also needs a `pyproject.toml` file. This file contains some
-metadata about hte package and informations about how to build a
+metadata about the package and informations about how to build a
 package. As the bare minimum the content of the `pyproject.toml` file
 specifies `setuptools` to be used for building the project:
 
@@ -80,15 +80,15 @@ build-backend = "setuptools.build_meta"
 
 With this `pyproject.toml` file, and `addition.py` and `__init__.py`
 in the `src/numerix` directory, you can install the `numerix` package
-on your machine and import it from whereever you want.
+on your machine and import it from wherever you want.
 
-For installation go to the project root, here `packagehowto/` and run
+To install the project, go to the project root, here `packagehowto/` and run
 from your shell
 ```sh
 pip3 install .
 ```
 This installs the package of the current project folder `.` somewhere
-in your home directory. From anywhere in your home directory you now
+in your home directory. From anywhere in your home file system you now
 can import this package. The import line of our `analyze.py` file
 needs to look like this:
 ```
@@ -97,6 +97,74 @@ from numerix.addition import add_two
 From the addition module of the numerix package the function add_two
 is imported.
 
+You would need to reinstall the package whenever you change your
+package, for exmple when you add a new function or when you just fix
+some package code. This is tedious, and that is why there is a `-e`
+option for `pip install`. So install your package with
+```sh
+pip3 install -e .
+```
+Then all future changes on your package are immediately available
+without the need to reinstall the package again.
+
+
+## The `__init__.py` file
+
+This file is your package. In fact, you could write a package that
+only has an `__init__.py` file in the package directory. All code you
+want to make available in you package could be place in the
+`__init__.py` file. For example, if you define a `add_four()` function
+in `__init__.py` like this:
+```
+def add_four(x):
+    return x + 4
+```
+then it can be imported directly from the package:
+```
+from numerix import add_four
+```
+
+Alternatively, you can define all your functions in module files, like
+we did with the function `add_two()` in the `addition.py` module. In
+the `__init__.py` file you can import this function and this way make
+it available directly from the package. With this line in `__init__.py`
+```
+from .addition import add_two
+```
+(note the `.` in front of `addition`!) you can import `add_two()`
+without specifying the module:
+```
+from numerix import add_two
+```
+
+
+## Multiple modules within a package
+
+You can have as many modules as you need in your package. Let's add a
+module `numbers.py` to the `numerix` package
+```txt
+    └── numerix
+        ├── __init__.py
+        ├── addition.py
+        └── numbers.py
+```
+with the following content:
+```
+from .addition import add_two
+
+def three():
+    return add_two(1)
+```
+This makes a function `three()` available that can be imported via
+```
+from numerix.numbers import three
+```
+
+Note, that the `numbers.py` module imports a function from the
+`addition.py` module via a relative import with the `.` in front of
+`addition`.
+
+
 
 
 
diff --git a/src/numerix/__init__.py b/src/numerix/__init__.py
index 28de7ae..2cec8f8 100644
--- a/src/numerix/__init__.py
+++ b/src/numerix/__init__.py
@@ -1,8 +1,27 @@
 """
 # Numerix
+
+Fancy numerics made easy.
 """
 
+# Functions defined directly in __init__.py can be imported directly
+# from the package (e.g. from numerix import add_four):
 def add_four(x):
+    """Add four to a number.
+
+    Parameters
+    ----------
+    x: int or float
+        A number.
+
+    Returns
+    -------
+    y: int or float
+       `x` plus 4.
+    """
     return x + 4
 
+
+# Functions from the modules of the package can be imported into the
+# namespace of the package:
 from .addition import add_two
diff --git a/src/numerix/addition.py b/src/numerix/addition.py
index bbb04bd..91dcf28 100644
--- a/src/numerix/addition.py
+++ b/src/numerix/addition.py
@@ -1,17 +1,6 @@
-from .numbers import one
-
-
-def __add_secret(x):
-    return x + 7
-
-
 def add_two(x):
     return x + 2
 
 
-def one_plus_two():
-    return add_two(one())
-    
-
 
 
diff --git a/src/numerix/numbers.py b/src/numerix/numbers.py
index 2db2139..c460463 100644
--- a/src/numerix/numbers.py
+++ b/src/numerix/numbers.py
@@ -1,9 +1,5 @@
+from .addition import add_two
 
-
-def one():
-    return 1
-
-
-def random():
-    return 4  # this number was obtained from a fair die
+def three():
+    return add_two(1)