The Triquetra:

The Triquetra is a triangular Celtic knot design which symbolizes all trinities, in Latin stands for "three cornered". The symbol has been found on 5000 year old Indian religious sites. In Europe the symbol itself dates as early as the eighth century on carved stones.

It has different meanings in each of those cultures but commonly represents eternity. For some it symbolizes life, death, and rebirth and the three forces of nature: earth, air, and water. It may symbolize the Celtic beliefs that everything has three distinct yet interlocked levels - physical, mental and spiritual.

Christianity re-invented the symbolism of three to mean the Father, the Son and the Holy Ghost. It symbolizes that the Holy Spirit is three beings of power, honor, and glory but is indivisibly one God. Triquetra itself is sometimes seen on the robes of Catholic priests.

The Claddagh:

The Claddagh symbol often seens on rings features hands holding a heart with a crown on top. Each element of the design symbolizes something. The heart of course is the symbol of love, the crown is loyalty, the hands are friendship.

It's a popular design which has a different meaning depending on how the person wears it. Someone who wears such a symbol on it's left hand with the heart inwards wants to show others that he or she has a life partner. Someone who wears it on his right hand with the symbol inwards shows he or she is in love but the symbol outwards means that the person is single.

The Claddagh is a Gaelic symbol goes back to the 1600's in Ireland in a village near Galway. The first known jewelry designer was a man called RIchard Joyce who came from that village. He could have designed it himself or seen it somewhere in his travels, nobody knows. They were used as wedding rings and passed from grandmother to granddaughter.