Jalaludin Rumi (1207-1273) was a Persian Sufi or mystic, a scholar, theologian, and poet. He is the most translated poet in the world. Rumi inherited a position from his father as head of a dervish learning community in Turkey. Coleman Barks, who has translated a great deal of Rumi's poetry, describes the community's purpose: "to open the heart, to explore the mystery of union, to fiercely search for and try to say truth, and to celebrate the glory and difficulty of being in a human incarnation."  Like Eckhart, Rumi was not cut off from the common world. He worked in the gardens and advocated for his students' needs, giving practical advice on all sorts of so-called secular matters. Perhaps this earthy grounding allowed Rumi to explore the very heights and depths of mystical experience.
Sufism is the mystical arm of Islam. Mainline Islam, like most organized religion, largely emphasizes external behaviors, whereas Sufism developed and emphasized the interior life.  According to Daniel Ladinsky, "the Sufis themselves say their 'way' has always existed, under many names, in many lands, associated with the mystical dimension of every spiritual system." The special emphasis of Sufism is "intense, often ecstatic, one-pointed devotion to God."  If you have ever seen a Sufi Dervish twirl around one pivot, as I was privileged to witness in Turkey, all the message is contained therein.
Rumi's experience of ecstasy was born in grief. It seems his beloved teacher and friend, Shams of Tabriz, was killed by jealous students. Rumi's sorrow led him into a yet deeper search for intimacy with the Divine. Ladinsky writes: "Rumi was inconsolable and began wandering, searching for any trace of his friend who was All-in-All to him. Finally he realized that his beloved Shams was within him. That is exactly the role of a Master, to create an intense desire for union with the Beloved--and when union happens, an atomic mystical power is released that can be directed toward humanity." 
Rumi often refers to the Divine Presence as a guest or a friend. Here is just one small jewel, translated by Coleman Barks, of Rumi's approximately 70,000 poems. 
One Who Can Quit Seeing Himself
I look for one simple and open enough
to see the Friend, not an intelligence
weighing several perspectives. I want
an empty shell to hold this pearl, not
a stone who pretends to have a secret
center, when the surface is all through.
I want one who can quit seeing himself,
fill with God and, instead of being
irritated by interruption and daily
resentments, feel those as kindness.