つまり

The word つまり can be used at the beginning of a sentence or phrase when you want to rephrase or restate something. It's generally translated as "in other words", "namely", "that means", or "in the end."

受験戦争というのは、つまり、いい学校に入るために、戦争のように勉強で競争することです。
In other words, the exam wars consist of a war-like competitive studying in order to get into a good school.

リーさんは今度の週末のパーティーに行きたくないって。つまり、私のことが嫌いんだ。
Lee-san said he doesn't want to come to the party this weekend. So really, he hates me.

登校拒否というのは、つまり、いじめなどの理由で学校に行かなくなるという意味です。
Namely, truancy means that you stop going to school because of things like bullying.

来月、日本で父の妹に訪ねに行くつもりです。つまり、彼女はおばさんですね。
Next month we're going to see my dad's little sister in Japan. So really she's my aunt.

なかなか～ない

Using the word なかなか + the negative form of a verb means that something occurred "not easily", "not readily", or just "difficult to..." It's generally used for negative situations where something you desire doesn't happen easily, or when something that's supposed to happen doesn't happen as it should.

一年生の時は漢字がなかなか覚えられませんでしたが、今は、あまり時間をかけずに覚えられます。
When I was a first year student I couldn't easily memorize kanji, but now I can memorize them without taking very much time.

もう１０年もピアノを練習しているが、なかなか上手に引けない。
I've already been practicing piano for ten years, but I still can't play it very well.

今年は十二月になってもなかなか寒くならない。地球温暖化のせいだろうか。
Even when we reach December this year it still won't get very cold. I wonder if it's due to global warming.

コンサートがなかなか始まらないので、客が怒り出した。
The concert was slow to start, so the audience broke out into a rage.

あるいは

The word あるいは can be used between nouns, phrases, or sentences to connect alternatives with an "either/or" type meaning. It's typically used in formal speech or written language.

この大学では、日本語、あるいは、英語で卒業論文を書くことになっている。
At this university, it's been decided that I will write my graduation thesis in Japanese or English.

日本に行くなら、いいホテルで、あるいは、ホストファミリで泊まると思うんだ。
If I go to Japan, I think I want to stay at either a nice hotel, or with a host family.

就職しようか、あるいは、大学院に進んで勉強を続けようか、今、迷っている。
Right now I'm torn between getting a full-time job, or moving on to grad school and continuing my studies.

リーさんは大学に行ったら、アメリカの歴史、あるいは、アメリカの文学を勉強すると言ってた。
Lee-san said that when he goes to university, he's going to study either American history or American literature.

一方

The word 一方 can be used to present two contrastive situations or concurrent states, either being used at the beginning of a sentence, or mid-sentence to connect the two ideas. It often translates as something like "on the other hand", "while", or "at the same time."

日本の義務教育は小学校が６年、中学校が３年である。一方、私の国では、小学校だけが義務教育で、中学校からは行っても行かなくてもいい。しかし、ほとんどの子供達は中学校に進学する。
As for Japanese compulsory education, elementary school is six years, and middle school is three years. On the other hand, in my own country, only elementary school is compulsory, and it's okay whether you go to middle school or not. However, almost all children go on to middle school.

カタカナは外国から日本に入ってきた言葉や、動物、花の名前など、特別な名詞に使われます。一方、ひらがなは、助詞や文末、送り仮名などに使われることが多いです。
Katakana is used for words that came to Japan from other countries, for animals, for things like the names of flowers, and for special nouns. On the other hand, hiragana is used a lot for things like particles, sentence endings, and okurigana.

子供達の学力が低下する一方で、受験戦争はますます激しくなっている。
Children's academic ability is declining, and yet at the same time we encourage "examination wars" more and more.

勉強が忙しい一方で、学費のためにアルバイトもしなければならないから、毎日本当に大変だ。
Studying is time-consuming, and yet because of tuition we have to get a part time job, so every day is really tough.

といった

The expression といった + X is used to present examples of X, where the examples are listed before the といった portion. It's similar to the phrases などの Noun and のような Noun, though といった can be preceded by nouns, nouns phrases, and entire sentences. It can generally be read as "like" or "such as."

日本語が上手に話せるようになるには、丁寧な話し方やくだけた話し方、敬語といったスピーチレベルが違う話し方の練習もしなければならない。
To reach a point where you can speak Japanese well, you must also practice the differing types of speech, such as polite speech, casual speech, and keigo.

リーさんの家では犬、猫、ねずみ、蛙といった動物がたくさん飼っていますね。
At his house Lee-san has lots of animals like dogs, cats, mice, and frogs.

どの国の言葉でも、丁寧になればなるほど文が長くなるといった傾向がある。
No matter the language, there are tendencies such as the more polite you get, the longer a sentence becomes.

娘さんは野菜や果物や肉といった食べ物が食べられるんだよ。
His daughter can eat foods like vegetables, fruits, and meat.

前者/後者

The words 前者 and 後者 mean the Japanese equivalent of the "former" and "latter", respectively. They're used to separately refer to two things that were previously mentioned in a sentence.

日本のお城と言えば、姫路城や大阪城が有名だ。前者は兵庫県にあって、後者は大阪府にある。
Speaking of Japanese castles, Himeji Castle and Osaka Castle are famous. The former is in Hyogo Prefecture, and the latter is in Osaka Prefecture.

今日はクラスで、アメリカでフロリダ州とカリフォルニア州について学んだ。前者はとても保守的で、後者は保守的じゃないんだよ。
Today in class, we learned about the states of Florida and California in the US. The former is very conservative, and the latter is not.

手塚治虫が描いたマンガでは「ジャングル大帝」や「ブラックジャック」が人気がある。前者は白いライオンの話で、後者はどんな病気でも治すことが出来る医者の話だ。
The manga "Great Emperor of the Jungle" and "Black Jack" by Osamu Tezuka are popular. The former is a story about a white lion, and the latter is about a doctor who can cure any kind of sickness no matter what it is.

日本の代表的な伝統芸能に能と狂言がある。前者は悲劇で後者は喜劇だ。
Noh plays and kyogen are representative of Japanese traditional arts. The former is a tragedy, and the latter is a comedy.

ても～なくても

The structure X ても X なくても can be used to express the Japanese equivalent of "whether or not." It can be used with nouns, verbs, and adjectives.

書いてあることが分かっても分からなくても、とにかく最後まで読んでみましょう。
Whether you understand what's written or not, let's at least try to read until the end.

あの女の人は優しくても優しくなくても、誘ってほしいな。
Whether she's kind or not, I still want to ask her out.

このアパートは家賃が安いから、静かでも静かじゃなくても、借りようと思っています。
Since this apartment's rent is cheap, I've decided I'm going to rent it whether it's quiet or not.

ドアが開いても開かなくても、その家に行くんだよ。
Whether the door opens or not, I'm going into that house.