Intelligence - Knowledge

Knowledge

How intelligent/smart is Batman? These are some of Batman's best feats of general knowledge in various areas. 

Showcasing his educational years its mentioned a young Bruce Wayne having learned to speed read, lip read, plus developing total recall (photographic memory) combined with his genius level intellect was able to ease through college having only taken the courses he needed then moved on (Shadow of the Bat #0)

Bruce having undergone F.B.I. training scored perfectly on every test except gun handling (Shadow of the Bat #0 & Secret Files of the World's Greatest Super Heroes)

Showing an example of how he can use his photographic memory to recall exactly how a previous battle he engaged in played out move for move in slow motion (Detective Comics #454)

Because of Disciple (a lunatic empowered by the Elder gods), the whole League got devolved. Despite being in a devolved mental state, Batman is still able to use intelligence & resourcefulness to become a formidable hunter and weapons creator/tool-maker as pointed out by Wonder Woman (JLA Primeval)

Batman v2 #22 - Backup Tale:

- Was taught and trained by a brilliant old Russian engineer named Sergei on how to build advanced weapons technology

- In his final test from Sergei, he's placed inside a dark closed off room (inside the Egyptian Sphinx) with limited oxygen supply and the tech he built in advance to prepare himself for the test which proved to be useless since they were broken

- Thinking outside the box and using his tech knowledge, he combines the non-operational tech to create unique high tech power gloves to dig his way out of the closed off room passing Sergei's test

Zen/Spiritual Body Manipulation Techniques

- Mentions that he's learned how to make 10 minutes of air last for an hour long through a steady breathing technique

Taught Tim Drake (Red Robin) the Possum Reflex which slows down the heart to restrict blood loss and ends up saving Tim's life (Battle for the Cowl #3)

While bleeding out, Red Robin thinks how Batman would likely go into a zen spiritual healing state and plot out his next 14 moves if Bruce was in his place (Red Robin #5)

After training 9 months "somewhere in the Himalayas" with Shihan Matsusa, known to be one of the greatest zen warrior monks, he is able to master Tummo meditation ("elemental battle between ice and blood" that takes place while he is meditating nearly naked outside), actually melting the ice he is sitting on (Detective Comics v2 #0)

During his training years before he became Batman, he underwent the Thogal Ritual which is an advanced type of meditation designed to simulate death and rebirth (Batman and Frankenstein #31)

He is able to enter a trance-like state, similar to coma, and to exit it at will (Gotham Underground #4)

Hypnosis/Mental Manuiplation 

Hypnotized himself into forgetting that he's Batman in order to protect his secret identity and outsmart Hugo Strange (Gotham Knights #11)

Shown using deep hypnosis against The General (aka General Eiling/Shaggy Man) who was vulnerable to psychological attack at the moment according to Batman but wasn't successful in using it due being interrupted (JLA #26)

Subdues an Ape Superman without physical force by using Neuro-linguistic Programming techniques (JLA Annual #3)

Seemingly uses a similar technique once again while Superman is in an enraged and devolved mental state using just his words to calm the more savage Superman down while other leaguers were prepared to use force (JLA Primeval)

Hacking

After quickly studying Mad Hatter's technology, he figures out the radio frequency that controls Hatter's flying buzz-saw hats then jams the signal and turns them right back against Mad Hatter (Detective Comics #573)

Hacks into and shuts down a high tech network using a device no more advanced than an average cell phone (Batman Inc. #4)

Despite Bludhaven's area is, as per Veteran's words, a communication's black hole, Batman still manages to contact him (Robin #146)

Takes control over the entire Gotham City communication system including Oracle's computers who's been locked out of her own system via Batman's hack (Catwoman v2 #35)

Hacks into the NASA database and downloads all their information into his computer (Batman The Abduction)

Hacks into Area 51 database (Batman Dreamland)

Using his highly advanced batcomputer he hacks into and accesses the secret files database of Interpol, all law enforcement, military, covert/black ops, and many other special operative agencies. In doing so, he's able to find out the true identity of a special operative who he recently encountered who's real name is Julia Pennyworth who officially doesn't even exist on the record (Batman Eternal #8-9)

Hacks into S.H.A.D.E.'s secret secure files without the organization knowing about it so he could locate Castle Frankenstein. He then reveals to Frankenstein that he's removed the S.H.A.D.E. Net implant from his neck so they would stay hidden from S.H.A.D.E. and prevent the organization from finding them (Batman & Robin v2 #19)

Hacks into the memory bank of an Manhunter android despite its advanced alien technology (created by the Guardians from the Green Lantern Corps) which he had never encountered before (Batman #415)

Quickly hacks into a kryptonian ship bypassing its encryption and recovering its logs (Superman Batman #64)

Alien Language

Has learned to speak Kryptonian as we see him speaking with Superman in his native alien language so their captors couldn't understand what they were saying and planning (Superman Batman #22)

Can speak (or "dabble") and understand the Kryptonian spoken language without a problem as seen here where he's talking to both Superman and the Daxamite Bi Sar in the Kryptonian language (Batman Superman #30)

Studying/Understanding

Able to pilot and use Lobo's alien spaceship seemingly without any trouble (Batman Superman #29)

Figures out how to use Rann Zeta-beam technology within a few minutes with Adam Strange pointing out that it took years for him to learn to use the technology (Brave and the Bold #6)

Studies the Starro bot made from advanced alien technology and quickly learns how it works plus how to use it to repel the Star Conqueror's invasion of earth (JLA #23)

After observing the effects a strange energy has on Superman's kryptonian powers that also caused Power Girl to lose control over her kryptonian powers as well, he quickly comes up with a solution to stop the effects of the strange energy using the kryptonite ring he bought as a contingency for Power Girl. However, this leaves the Man of Steel no more powerful than the average human due to the seemingly overwhelming energies in his body balancing each other out which proves his theory to be correct (Worlds Finest #20)

Quickly deduces how Know Man's technology (given to him by a Controller who are an ancient advanced alien race) works after studying it only for a short amount of time then he comes up with a plan using the same tech and his league teammates to free the trapped minds of everyone on earth (Justice League: A Midsummer's Nightmare #3)

Despite the super advanced New God technology that's built inside a Mother Box it's revealed by Batgirl and Red Hood that he managed to modify the Mother Box he originally took from a Parademon, figure out the coordinates of where Apokolips is located, and use the Mother Box to boom tube himself to Apokolips (Batman & Robin v2 #35)

Other/Misc

While in Bhutran (or Bhutan) during his training years, he spent 3 months studying with the 10 Eyed Men learning how to kill demons (Superman #710)

Made a surgical incision in his own palm a long time ago in advance to cleverly hide a special tool for later use showcasing some his medical knowledge and skill (Batman Annual v2 #2)

Knows the general location of where even the hidden continent of Atlantis is located which amazes his Justice League teammate Aquaman (the King of Atlantis) who he's seen dropping off within close range of where Atlantis can be exactly found (Aquaman #32)