A conjunction is an invariable element that links other elements within the sentence. Just as the preposition it has no meaning by itself. Some common phrases that are used to express a contrast between one idea and another include:

sin embargo - however
no obstante - nevertheless, in spite of
a pesar de - despite
de todos modos - anyway
aunque - even though, although

Let's look at some example sentences.

No debió hacerlo, sin embargo lo hizo.
He should not have done it, however he did it.

Aunque ha logrado todo no obstante es infeliz.
Although he has achieved everything, nevertheless he is unhappy.

A pesar de todo, te has equivocado.
Despite everything, you have made a mistake.

A pesar de la lluvia, fue al parque.
Despite the rain, he (she) went to the park.

Aunque el piso esté lejos del centro, me gusta.
Although the apartment is far from downtown, I like it.

Aunque esté bien situado, es pequeño.
Although it's a good location, it's small.

Aunque no sabe ni leer ni escribir es feliz.
Although he/she does not know how to read or write, he/she is happy.