Superwörter--I

DAMIT, SO DASS, UM...ZU

1a. The da-compound damit means "with it" or "with that."

Magst du den SPAM? Ich wollte dir damit eine Freude machen.
Do you like the SPAM? I wanted to make you happy with it.

Der neue Porsche hat einen Kernkraftmotor. Damit kommt er in 0,1 Sekunden von 0 auf 100 km/h.
The new Porsche has a nuclear powered engine. With it, it goes from 0 to 100 km/h in 0.1 seconds.

Note that for the relative pronoun "with which," you cannot use damit:
Eli Whitney hat eine Maschine erfunden, mit der damit man Baumwollfasern von den Samen trennen kann.
Eli Whitney invented a machine with which one can separate cotton fibers from seeds.

Der neue Porsche hat einen Kernkraftmotor, mit dem damit er in 0,1 Sekunden von 0 auf 100 km/h kommt.
The new Porsche has a nuclear powered engine with which it goes from 0 to 100 km/h in 0.1 seconds.

If it is associated with a prepositional verb, damit can function as an anticipatory da-compound. In this case, it would usually be redundant in the English translation:
Ich bin damit zufrieden, daß der 1. FC Köln mehr als die Hälfte seiner Spiele gewonnen hat.
I am satisfied (with it) that 1. FC Köln won more than half of its games.
1b. The subordinating conjunctiondamit means "so that." It stands at the beginning of the clause, and the conjugated verb comes at the end:
Fledermäuse benutzen Ultraschall, damit sie nicht in die Wände ihrer Höhlen fliegen.
Bats use ultrasound so that they don't fly into the walls of their caves.
2. Um...zu also means "so that," but it is more natural to translate it as "in order to." It can only be used if both clauses have the same subject:
Ich esse Spinat, um stark zu werden./Ich esse Spinat, damit ich stark werde.
I eat spinach in order to become strong/I eat spinach so that I will become strong.

Du isst Spinat, damit ich glücklich bin. (Cannot use um...zu here. Could you use it in example (1b) above?)
You eat spinach, so that I will be happy.

The English equivalent is often simply "to":
Ich bin intelligent genug, um Barney zu hassen.
I am intelligent enough to hate Barney.
3. So dass also means "so that," but unlike damit and um...zu, it emphasizes the result of the action, not the purpose. Compare:
 
Das Quiz war verwirrend, so dass die Studenten schlechte Noten bekamen. Das Quiz war verwirrend, damit die Studenten schlechte Noten bekamen.
The quiz was confusing, so that [as a result] students got bad grades. [The teacher probably did not intend for this to happen] This would mean that the teacher intentionally made the quiz confusing so that the students would get bad grades. Teachers aren't that evil ]
Yao Ming ist 2,26 groß, so dass er selten übersehen wird. Yao Ming ist 2,26 groß, damit er selten übersehen wird.
Yao Ming is 2.26 m tall, so that [as a result] he is rarely overlooked. This would mean Yao Ming chose to be so tall, in order not to be overlooked.
UM

1. Um...zu means "in order to"--see above.

2. Um can mean "at" with reference to a certain time "of the clock" (o'clock):

Die Nachrichten sind um 8 Uhr.
3. Um can mean "around" both in the literal sense (in this sense it is often used together with herum) and occasionally in the sense of "approximately" or "about"  (in this sense it is often used with "die" for plural quantities, especially with prices and times).
Wir fahren um Ulm herum.
We’re driving around Ulm (Could mean we are avoiding Ulm, or that we are driving around in Ulm).

Wir treffen uns um die 4 Uhr.
We’re meeting at around 4 o’clock. [here, die must be used to indicate approximate, rather than precise, time]

Ich gehe um die Ecke.
I’m going around the corner.

Die Temperatur war um 8 Grad. [here, die is optional]
The temperature was around 8 degrees.

4. Es geht um... means "It is about" (as in "topic" or "what’s at stake"). Es handelt sich um is similar. Both must be used with "es" as the subject: "Der Artikel geht um..." is wrong.
Es geht um Leben oder Tod./Es handelt sich um Leben und Tod.
It is a matter of (about) life or death

In dem Artikel geht es um Evolution.
The article is about evolution.

[Do not use handelt es sich um to say what an article is about. You can, however, say "Der Artikel handelt von Evolution."].

5. Um can mean "by" when changes in a quantity are being indicated:
Wenn wir das Volumen eines Gases um 10% senken und die Temperatur konstant halten, steigt der Druck um 10%.
If we reduce the volume of a gas by 10% and keep the temperature constant, the pressure rises by 10%.
6. Je ..., um so... means "the...the" with comparisons. Je...je and je...desto are similar.  Note the verb position: the conjugated verb comes in final position in the "je" clause, and in position two in the "um so" (or "je" or "desto") clause (in the latter clause, "um so" (or "je" or "desto") occupies position zero).
Je mehr deutsch ich lerne, um so glücklicher werde ich.
The more German I learn, the happier I become.
7. Certain prepositional verbs take the preposition um, in which case the translation will vary. Some common examples:
sich bemühen um to concern oneself with
sich bewerben um to apply for
bitten um to ask for
kämpfen um to fight for something [in order to obtain it]
sich kümmern um to concern oneself with someone/something [devoting attention, taking care of]
sich sorgen um to worry about
sich streiten um to argue about something [in order to obtain it]

NACH/LAUT/GEMÄSS/ZUFOLGE/SO

In addition to their other meanings, these can all mean "according to."

  Case used Position before or after source Pronoun sources?
nach dative before or after yes
laut dative (rarely genitive) before no
gemäß dative always after pronouns, mostly after nouns yes
zufolge dative after yes
so nominative before no
Nach/laut/gemäß/zufolge dem Artikel ist die Erde flach [=flat]
According to the article, the earth is flat

Nach/laut/gemäß/zufolge ihm/ihr ist die Erde flach
According to him/her, the earth is flat

Dem Artikel nach/laut/gemäß/zufolge ist die Erde flach
According to the article, the earth is flat

Ihm/ihr nach/laut/gemäß/zufolge ist die Erde flach
According to him/her, the earth is flat

Nach ihr/Ihr gemäß/Ihr zufolge kam das Huhn vor dem Ei.
According to her, the chicken came before the egg.


Whereas nach/laut/gemäß/zufolge state the source before stating the opinion/fact derived from the source, so states the source afterwards. So sometimes implies a little more doubt.

Die Erde ist rechteckig [rectangular], so der Artikel.

Das Baby hatte den Kopf von Elvis, so die BILD-Zeitung

JENER/DIESER; ERSTERER/LETZTERER

These both mean "the former/the latter" in that order. Jener and dieser are der-words ==> they follow the same pattern of endings as der/die/das; ersterer and letzterer are adjectives ==> they take adjective endings.
 

Gottlieb Daimler und Carl Benz waren Pioniere der Autoindustrie: jener/ersterer entwickelte den ersten schnelllaufenden Fahrzeugmotor, und dieser/letzterer baute das erste moderne Automobil. Gottlieb Daimler and Carl Benz were pioneers of the automobile industry: the former developed the first fast-running internal combustion engine, and the latter built the first modern automobile.
Es gibt zwei Arten von Ottomotor: Zweitaktmotoren und Viertaktmotoren.  Diese werden in den meisten Autos benutzt, jene zum Beispiel in Motorrädern und Kettensägen. There are two types of otto engine [i.e. "conventional" internal combustion engines, as opposed to diesel and rotary engines]: two-stroke and four-stroke engines.  The latter are used in most cars, the former in motorcycles and chainsaws, for example.
Die wichtigsten Verbrennungsmotoren sind der Ottomotor und der Dieselmotor.  Ersterer/Der erstere wurde von Nikolaus Otto erfunden, letzterer/der letztere von Rudolf Diesel. The most important types of internal combustion engine are the otto engine and the diesel engine.  The former was invented by Nikolaus Otto, the latter by Rudolf Diesel.