The summer anime slate has a lot of promising isekai shows and one of which is How a Realist Hero Rebuilt the Kingdom, also known as Re: CONSTRUCTION - The Elfrieden Kingdom Tales of Realistic Brave or Genjitsu Shugi Yuusha no Oukoku Saikenki. Here is the current status of the series on whether the manga where it is based is already complete, finished, or still ongoing.
It follows the story of Kazuya Sōma who has been summoned by the Kingdom of Elfrieden when they performed a ritual for a brave man to arrive. Kazuya lived his previous life as a humanities student and he has knowledge of realism and Machiavellianism before getting transported to another world. King Alberto, the ruler of the kingdom, saw the qualities he had and why he was the one summoned. Now, Kazuya would have to deal with the problems of the kingdom applying his knowledge from his former life.
The anime adaptation of How a Realist Hero Rebuilt the Kingdom by J.C. Staff is directed by Takashi Watanabe, written by Gō Zappa and Hiroshi Ōnogi, characters designed by Mai Otsuka, and music by Akiyuki Tateyama wherein the show opens with "Hello Horizon" by Inori Minase, and ends with Aimi's "Kazanear."
How a Realist Hero Rebuilt the Kingdom releases new episodes weekly on Funimation, and despite having no confirmation yet as to the English dubbed version, it is available with English subtitles on top of the original Japanese dub. Those with premium access on Funimation for the price of $5.99 per month or $59.99 a year get first dibs of the runs of the show. It will have 13 episodes all in all.
Is How a Realist Hero Rebuilt the Kingdom Manga Complete, Finished, or Ongoing?
First, it is based on the Japanese light novels of Dojyomaru illustrated by Fuyuyuki published by J-Novel Club and Seven Seas Entertainment. It originally started as a web novel on Shōsetsuka ni Narō, however, it was deleted and published by Overlap Bunko in 2016 later on. To date, there are 15 volumes of light novels.
There is also a shōnen manga adaptation of How a Realist Hero Rebuilt the Kingdom by Satoshi Ueda and it was also digitally available from the same publisher as that of the light novels. It has 5 volumes so far, and both are still ongoing.