One of the problems people have in discussion of Religious ideas, most of all with Catholic and Orthodox ideas, is they think in the terms of the 21rst Century, and the vocabulary of the 21st Century. If we think of Mystery as only a puzzle to be solved, or something that we can’t find an answer to, we are thinking in modern terms. If we include in the definition of Mystery the traditional meaning in religion, that beyond the outward appearence there are greater truths, as we grow spiritually we understand, and will know fully when we see God face to face in heaven.
With regard to mysteries of the rosary or religion in gereral, we can look at the Incarnation. To our human eyes we see a baby born. The mystery here is that God Himself became incarnate, and came to the world as Truly God and Truly Man in the person of Jesus. Not 50% God and 50% Man. Not as simply God taking over the body of a man. But the incarnation of the creator of the world. Over years of study and prayer we come to understand better this mystery, with the promise of knowing and understanding it fully when we see God face to face in heaven.
Traditionally the “full” rosary is praying 15 decades. A decade consists of ten Hail Mary’s, one Glory be to the Father, and one Lord’s Prayer. In recent times five more mysteries where added the Lumenous Mysteries, however these can be included or not depending on the individual’s desire to include them or not.