docs(manual): write content for observer.md

doc/observer.md

@@ -1,5 +1,49 @@
 # Observer
 
-What is an Observer?
+**What is an Observer?** An Observer is a consumer of values delivered by an Observable. Observers are simply a set of callbacks, one for each type of notification delivered by the Observable: `next`, `error`, and `complete`. The following is an example of a typical Observer object:
 
-TODO
+```js
+var observer = {
+  next: x => console.log('Observer got a next value: ' + x),
+  error: err => console.error('Observer got an error: ' + err),
+  complete: () => console.log('Observer got a complete notification'),
+};
+```
+
+To use the Observer, provide it to the `subscribe` of an Observable:
+
+<!-- skip-example -->
+```js
+observable.subscribe(observer);
+```
+
+<span class="informal">Observers are just objects with three callbacks, one for each type of notification that an Observable may deliver.</span>
+
+Observers in RxJS may also be *partial*. If you don't provide one of the callbacks, the execution of the Observable will still happen normally, except some types of notifications will be ignored, because they don't have a corresponding callback in the Observer.
+
+The example below is an Observer without the `complete` callback:
+
+```js
+var observer = {
+  next: x => console.log('Observer got a next value: ' + x),
+  error: err => console.error('Observer got an error: ' + err),
+};
+```
+
+When subscribing to an Observable, you may also just provide the callbacks as arguments, without being attached to an Observer object, for instance like this:
+
+<!-- skip-example -->
+```js
+observable.subscribe(x => console.log('Observer got a next value: ' + x));
+```
+
+Internally in `observable.subscribe`, it will create an Observer object using the first callback argument as the `next` handler. All three types of callbacks may be provided as arguments:
+
+<!-- skip-example -->
+```js
+observable.subscribe(
+  x => console.log('Observer got a next value: ' + x),
+  err => console.error('Observer got an error: ' + err),
+  () => console.log('Observer got a complete notification')
+);
+```