1. Zwar is usually "concessive" and may be translated as it is/may be true that or although. In this sense it must be followed by aber or an equivalent word (jedoch in the first example below).
It may be true that some [of his] contemporaries also made (OR: Some of his contemporaries did also make) cross-breeding experiments, but with quite confusing results.
Ich bin zwar müde, aber ich möchte trotzdem kein Koffein.
It is true that I am tired, but nevertheless I don't want any caffeine (OR: Although I am tired, I don't want any caffeine).
Tridacna hat zwar keinen Kopf, aber sie ist dennoch recht kompliziert.
Although Tridacna has no head, it is nevertheless quite complicated.
2. Und zwar introduces a specification, i.e. more specific information about the statement preceding it (not just more information--see below!). It is a useful expression for which there is no good English equivalent. Sometimes, it is best not to translate it at all. It can sometimes be translated as namely (in which case it is equivalent to nämlich in the first sense below), in fact, actually, or to be specific.
There are four seasons, namely summer, autumn, winter and spring.
Ich habe Hunger, und zwar sehr.
I'm hungry, very hungry in fact/actually.
Sie hat sich verletzt, und zwar am Bein.
She injured herself, her leg, to be specific.
Er war verwirrt, und zwar so sehr, daß er Französisch lernen wollte.
He was confused; so much so (in fact/actually), that he wanted to learn French.
Note: Sometimes und zwar (or nämlich) cannot be used in this way, especially if you could say "for example," "such as," or "especially" in English:
Ich mag Musik, und zwar Trance und Techno.
Ich mag Fleisch, und zwar Rindfleisch.
These examples would work if you introduced something into the initial clause that would lead the listener/reader to expect a specification:
Ich mag nur zwei Arten von [=only two types of] Musik, und zwar/nämlich Trance und Techno.
Ich mag nur eine Sorte [=just one type of] Fleisch, und zwar/nämlich Rindfleisch.
1. Doch contradicts negative statements and questions:
I've fallen and I can't get up.--Yes you can!
Hast du Elvis heute nicht gesehen?--Doch!
Did you not see Elvis today?--Yes I did!
2. Doch can mean nevertheless [its position in the sentence follows the rules for nicht]:
We made it [i.e. succeeded] nevertheless!
Ich soll nicht jodeln, aber ich tue es doch.
I'm not supposed to yodel, but I do it nevertheless.
3. Doch can be the equivalent of a rhetorical but in the following sense:
But what will happen when we do that?
Doch stimmt das wirklich?
But is that really true?
4. Doch can also be used as a flavoring particle to mean after all, to express impatience or irritation and more, but we will not study this in detail.
1. Nämlich can mean namely, in which case it is very similar to und zwar. Where you cannot say namely in English, you should use und zwar, and not nämlich, so in the above examples for und zwar, nämlich could have been used only in the first sentence. Unlike und zwar, nämlich can sometimes follow the noun it modifies:
The newspaper comes once a week, namely on Friday.
2. Nämlich can mean for, indicating a reason in the sense of for the fact is that:
She never learns the vocabulary, for (the fact is that) she has no time for that.
Während nämlich bei der Wunderblume die Anlagen für "Rot" und "Weiß" gleich starken Einfluß ... haben, überwiegt bei der Erbse der Einfluß von Rotviolett.
For (the fact is that) while in the case of the Wunderblume the genes for "red" and "white" have an equally strong influence, the influence of reddish purple predominates in the case of the pea.
3. Occasionally, especially in older German, nämlich is an adjective and means the same. Note that to use nämlich in this way now would be quite formal.
The strong verbs in the imperfect tense have the same endings as the modal verbs in the present tense.
Wir wiederholten das Experiment, mit dem nämlichen Resultat.
We repeated the experiment, with the same result.
Unter can actually have a variety of specific meanings in addition to the most common one of "underneath." Of these, the most important one for our purposes is that unter can mean among. Unter is an either/or preposition, but when it is used in this sense, it always takes the dative.
There are no prokaryotes (single-celled organisms) among the students in our class.
Bei Kreuzung reinerbiger Stammformen sind die Nachkommen unter sich gleich.
In the case of a cross-breeding of pure-bred original specimens, the descendants are identical among themselves [i.e. the descendants all look alike].
Von diesen zahlreichen Typen von Reptilien brachten lediglich zwei Nachkommen hervor, unter denen man einigen ein gewisses Maß an Intelligenz zuschreiben kann.
Of these numerous types of reptiles, only two generated descendants among whom one can ascribe to some a certain measure of intelligence.
In addition to its usual meaning of "beside,"neben can mean besides. Neben is an either/or preposition, but when it is used in this sense, it always takes the dative.
Besides its teeth, the killer rabbit also uses its paws and ears against its victims.
Die Algen produzieren neben Sauerstoff auch Nährstoffe für Tridacna.
Besides oxygen, the algae also produce nutrients for Tridacna.
Note: Neben can only be used in this way as a preposition, i.e. you can use it to say "Besides X" where X is a noun; X cannot be a whole clause including a verb. When you want to introduce a whole clause including a verb with besides in English, you would usually use nicht nur ..., sondern auch in the corresponding German sentence. Here are some examples of when you could and could not use neben to mean besides in similar contexts:
Besides being a philosopher and a theologian, Albert Schweitzer was a good organist. [Besides introduces the whole clause "being a philosopher and a theologian" ==> cannot use neben]
Neben Philosophie und Theologie beherrschte Albert Schweitzer auch das Orgelspielen.
Besides philosophy and theology, Albert Schweitzer had also mastered organ playing. [Besides introduces only the nouns "philosophy and theology" ==> can use neben (this sentence could also be translated using nicht nur ..., sondern auch)]
Ich habe nicht nur meine Hausaufgabe vergessen, sondern auch die Vokabeln nicht gelernt.
Besides forgetting my homework, I have also not learned the vocabulary. [Besides introduces the whole clause "forgetting my homework" ==> cannot use neben]
Neben den Hausaufgaben habe ich auch mein Buch vergessen.
Besides the homework I also forgot my book. [Besides introduces only the noun " the homework " ==> can use neben(this sentence could also be translated using nicht nur ..., sondern auch)]