Dr. John Brady is working at the Castle Hill government laboratory investigating the nature of refraction - his experiments achieve success when he is able to make a rat become invisible - but a leak in the containment chamber releases the radation into the lab, and Brady finds himself rendered completely invisible as well. At first put under lock and key by the government, he escapes and runs to his former colleague Dr. Crompton for help, but finds that the powers of invisibility have the potential to corrupt...

The first episode begins very quickly, with Brady becoming invisible in the first moments. Fortunately they give time to introduce and develop Brady and his family before the action starts - already however, the 25 minute runtimes of these episodes starts to show itself, and the pacing does seem a little rushed.

Brady is working hard to find a cure for his invisibility but needs a human volunteer. He is tricked into travelling to the house of the exiled South American industrialist Raphael Constantine. Hideously scarred by a grenade the man appeals to Brady to use him in the experiments as he yearns for invisibility. However, it soon becomes clear that Constantine has a more sinister purpose in mind for his powers...

An outspoken Russian scientist speaking in London is kidnapped by secret agents and locked up in the embassy. Brady follows her and breaks into the embassy before beginning a diplomatic attempt to have her freed. When this fails he sneaks her out of the building to his own house, but finds that the Russian ambassador is not going to give up the chase easily...

After a serious car accident witnessed by many people, the government reveal Brady's invisibility to the press and he becomes a near-celebrity figure hounded by the media. Meanwhile the friend of his young niece begins to suspect that her stepfather is planning to murder her mother for the inheritance and pleads with Brady to help...

Barbara Crane, a respected theatre actress, finds herself the subject of bribery after accidentally running down a man on a clifftop road. Worried by the events she starts to perform badly, and a suspicious Brady decides to investigate further, discovering that there is more than simple blackmail going on...

A Russian sailor makes a bid for freedom from a trawler at anchor in a British harbour, but is soon captured and taken back to the ship. The head of the refugee committee appeals to Brady to help them and although reluctant to assist, he soon decides to sneak on board the ship and find out what he can do to help - however, it soon turns out that Brady has been set up, and he is ambushed by the sailors as the ship heads back towards Russia.

A group of criminals raid an important British atomic laboratory and photograph some key documents onto microfilm. When the customs officers quickly clamp down on passengers leaving the country, one of the men hides the film in the mink coat of the ventriloquist performer Penny Page who is flying to Paris. When Brady's sister Diane witnesses this, the pair find themselves drawn into a deadly game as the criminals try to get the invaluable film back from Mrs Page.

When an airline pilot is framed for importing drugs into the country, he phones his old friend Peter Brady for help. Before Brady arrives however, the pilot is shot and badly injured in front of his wife, who is blind. Brady helps the police with their investigations and devises and elaborate plot to find the killer...

When the reformed career criminal is framed for an armed robbery and sent to prison again, he is determined to get free and prove his innocence and escapes 5 times before being recaptured. Curious about the story, Brady decides to investigate and helps the man to escape again to discover the truth behind the conviction...

Brady's fame leads to trouble when a group of criminals kidnap his young niece and hold her hostage - forcing Brady to commit a bank robbery.

When one of Brady's colleagues announces that he will not be returning from his holiday in Italy, and is seen using his mathematical talents to win at roulette, Brady decides to fly out and convince him to return - but he soon discovers that Professor Owens is working to save his daughter who is being held hostage by the mob...

After his bag of documents was stolen, Brady is kidnapped by a mysterious man who wants him to commit a murder - and to keep the unseen Brady in check, he has a vicious guard dog who can sniff out and catch even an invisible man.