English has many ways in which you can connect two sentences or even two paragraphs to either emphasize a point you are trying to make or simply make things clearer to understand. Lets take a look at some of them.

Showing contrast:

However:
- I am going to just relax all holiday. However, my wife will continue to work.
Nonetheless/ nevertheless:
- The economy is getting worse. Nevertheless, People keep shopping and spending.
On the other hand:
- Japanese trains are very punctual and clean. On the other hand, they are usually very crowded.
On the contrary:
- I don't hate umeboshi. On the contrary, I really like them.

Showing similarity:

Likewise:
- Walking alone through the streets in some areas is not recommended. Likewise, jogging alone at night can be dangerous.
Correspondingly:
- The Price of train tickets are going to become more expensive. Correspondingly, bus companies will also raise their prices.

Showing result:

Therefore:
- My uncle won the lottery last year. Therefore, the whole extended family is going to Hawaii this summer.
  - Thus:
- My company went bankrupt. Thus, I have to seek other employment.
As a consequence:
- My brother was diagnosed with diabetes last week. As a consequence he can't eat a lot of sweets nor drink a lot of alcohol anymore.