The Singhasari Kingdom was founded by the semi-legendary Ken Arok, who appears in the literature as something of a trickster character, who gets his way by being quick of wit and somewhat treacherous. He killed the King of a previous dynasty, and took his lovely wife for his own: this was the famous Ken Dedes, now immortalised as Prajñāpāramitā in one of the finest statues produced in Java.
He was followed by four more kings, culminating on Kertanagara, who was also the hero of Nagarakertagama, one of the classical poems (kakawin, or kawi) of Old Javanese literature. He was eventually overthrown through treachery and his successor also killed, before Kertanagara’s son Raden Wijaya, founded the succeeding Majapahit Kingdom.
The capital of the Kingdom lies in a fertile highland valley around 7km north of present day Malang, and is still called Singosari (an alternative spelling for the name), but the kingdom itself spread its influence all over East Java and outlying islands, and they controlled the sea passages as well, as the map below shows.

Map Drawn by Gunawan Kartapranata (CC BY-SA 3.0 licence)
It was during the Singhasari Period that the Pamalayu Expeditation took place, under the Generalship of Admiral Mahesa Anabrang, which sought to protect the Maritime Silk Roads, and prevent the incursion of the Mongol forces, which were just then conquering the largest empire ever known. In the end the Mongols, although they invaded, were not able to conquer Java.
Many of the temples and other historical monuments built during this time still exist, in various states of repair. Temples were often built to house the post-mortem deification of a King as Visnu, or some other god. The temples are mainly of the syncretic Śiva-Buddha religion, which was also founded during this period, and lasted till the end of the Majapahit period, a few centuries later.
I have two collections of materials, and one dedicated album. The collections come from the Pasuruan District (44 photos) and the Malang District (81 + 3x 360°), and show representative remains from the candis that have been restored. It should be noted that this is only a selection, as there are literally scores of candis in these areas.
The dedicated album is of the very interesting Candi Jago (121 + 3x 360°), which has some of the finest relief work in Java outside Borobudur. The reliefs here though show the influence of the Wayang puppet theatre in presentation, and retell various Hindu, Buddhist and folklore stories.
There are maps, and other in-depth information on each page, which describe the various candis, and give further information about the history and literature of the Period.