During the month-long Israeli incursion into Lebanon in 2006, various useful idiots in Britain declared, ‘We are all Hezbollah now’, while the former Labour MP George Galloway pronounced that Hezbollah was not a terrorist organisation. More seriously, the UK government still refuses to join many others in condemning Hezbollah tout court as a terrorist entity, reserving that designation solely for its ‘military wing’.

That slippery stance will be much harder to maintain if bureaucrats and politicians read Matthew Levitt’s detailed and gripping new study of Hezbollah’s global operations. Levitt was deputy assistant secretary for intelligence and analysis at the US Department of the Treasury, from which vantage he has authored many scholarly articles on the financing of international terrorism. This excellent book should help anyone under any illusions about what Hezbollah really is to come to their senses.

Established in the mid-1980s, the Party of Allah (which is what Hezbollah means) was an Iranian-sponsored amalgamation of several Shi’a militant grouplets in Israeli-occupied southern Lebanon. Thus it could claim to be the ‘resistance’, a claim still made long after Israel has withdrawn from that theatre.

Hezbollah is polycephalous: it includes a Shi’a spiritual and welfare apparatus; a party with a locking veto on Lebanese political life; and a powerful army, currently providing Syria’s President Bashar al-Assad with light infantry capabilities. The global terrorist machine called Islamic Jihad Organisation is said to have been subsumed by Hezbollah.

The last two entities take their marching orders from the Iranian Revolutionary Guard Corp (IRGC) – and hence ultimately from Supreme Leader Ali Khamenei – and act in dangerous liaison with the IRGC’s external operations arm, the Quds Force, the current chief of which, General Qassem Suleimani, is directing Assad’s war effort.

Until a Mossad bomb in the headrest of his Mitsubishi blew his head off after he had left a reception at the Iranian embassy in Damascus in 2008, one Imad Mughniyeh was the main interface between the Quds Force and Hezbollah’s global terrorist operations. From Tehran’s perspective, the asymmetric uses of Hezbollah in its war on the US, Israel and others is worth its annual subvention of $200 million a year. That buys a lot of mayhem and vengeance. Perhaps because of his bureaucratic background, Levitt’s account is at its best – and it is very good indeed – when he follows the money that has paid for several decades of shootings and bombings the world over.

Hezbollah has seeded itself amid a far-flung and often enterprising Lebanese Shi’a diaspora, which seems to thrive in such delinquent environments as the Tri-Border area, where Argentina abuts Brazil and Paraguay, and such corrupt African states as Benin, Democratic Republic of the Congo or Guinea-Bissau. Fluid borders enable Hezbollah’s masterminds to direct terrorist operations from outside the countries where the bombs go off and to make their getaways long before the explosions.

Rather like the Boston Irish and the IRA, these local Lebanese are easy to menace with threats against their relatives in Lebanon or to coopt with stirring tales of martyrdom from the old homeland. Some are also greedy for the profits that come from trafficking cocaine from Latin America to West Africa (and thence up into Europe and the Middle East) and shipping conflict diamonds from Sierra Leone to Antwerp. In this murky world, laundered money moves not in suitcases but by the pallet-load, as a few inadvertent air crashes have revealed, or else it is recycled into the huge trade in second-hand cars destined for West Africa (it is even sometimes hidden inside the tyres).

Of course, Hezbollah is also active in more civilised jurisdictions. In the US its Michigan-based cells have been involved in credit-card scams – in which teams of specially recruited single mothers buy laptops by the carload – as well as everything from interstate evasion of duties on truckloads of cigarettes to (very lucrative) knockoff Viagra and counterfeit Barbie dolls.

With grim attention to detail, Levitt describes what this money buys. On 18 July 1994 a suicide bomber, driving a Renault van laden with explosives, demolished most of the Asociación Mutual Israelita Argentina in Buenos Aires, killing 85 people and injuring 150 more. The plot was masterminded by one Mohsen Rabbani, an Iranian who led prayers at a Shi’a mosque and was in the country acting on behalf of Tehran’s Ministry of Agriculture, supervising the quality of meat exported to his homeland. He had attended a meeting in Mashhad in Iran in August 1993 where the decision to carry out this attack was taken; the other participants were the Supreme Leader, President Akbar Rafsanjani, the head of the Ministry of Intelligence and Security, and Foreign Minister Ali Velayati, a hardline candidate in Iran’s 2013 presidential elections.

Rabbani was given diplomatic status so that he could plan the attack under cover of immunity. After the bombing, huge numbers of calls were found to have been made between Buenos Aires and the Tri-Border area to which Rabbani had relocated himself, and from the Iranian embassy in Argentina to ‘cut-out’ numbers in Iran that masked the Foreign and Security ministries. Several Iranian diplomats flew the Buenos Aires coop days before the bombing, all using newly issued and sequentially numbered Iranian diplomatic passports.

And so Levitt’s book goes on, through shootings of Iranian dissidents in Berlin, London, Paris and Vienna by Hezbollah assassins, to atrocities such as the 1996 Khobar Towers bombing in Saudi Arabia, which, involving 20,000 pounds of TNT, was the largest non-nuclear explosion then on record, and so loud that it was felt twenty miles away in Bahrain. This is not to mention serial aircraft hijackings and kidnappings. Effective counterterrorist measures in the interim mean that Hezbollah has had to divert its attempts to kill Americans and Israelis to such softer targets as Azerbaijan, Bulgaria, Thailand and Turkey, many of them ‘revenge’ attacks on Israeli tourists for the killing of Mughniyeh.

Stringent international sanctions have resulted in the election of Hassan Rouhani, the smiling Iranian president, and a window of willingness to negotiate the limits of Iran’s nuclear weapons programme. But we should never forget that Iran has Hezbollah as its accomplice, albeit one temporarily diverted by Iran’s pressing need to help Assad slaughter Syria’s Sunni rebels, some of whose own bravest fighters, ironically enough, come from circles close to al-Qaeda. They deserve each other.