You are either very lucky or very unlucky, because this is my absolute favorite topic.

This chapter of Sino-German relations really starts in 1919, at the end of World War I. At the time, because of the nature of the peace, Germany had become completely and utterly diplomatically isolated from the rest of the world. The government was weak, and a significant amount of power was held by either "Soldiers and Workers Councils," organized movements like the Spartakists, or even outright militias like the Freikorps. Many former German officers drifted off to other countries, especially after the failed right-wing coup attempt known as the Kapp Putsch. These countries included Eastern Europe, Russia, the Middle East, and of course, China. While China had declared war on Germany in World War I, the central government had relatively little control and significant power was in the hands of local warlords and cliques, one of which was the Kuomintang (also known as Guomindang, or Chinese Nationalists, or KMT).

One of these officers who eventually drifted over to China was a former General of Artillery named Max Bauer. The KMT had approached Bauer with a proposal to work as a military adviser to help modernize the KMT forces. The long-term goal was to use his connections as an artilleryman to acquire large artillery pieces that China could not make at the time.

At this point in Germany, there were really two major organizations performing foreign policy. While the government was still normally in charge of diplomatic relations, the Reichswehr, the Weimar Republic army, was also conducting foreign policy of its own, albeit informally. This was the phenomenon known as "state within the state". This meant that the Reichswehr could essentially conduct its own informal agreements as it pleased, so long as it did not go against the government. While Bauer and other members of the German military that had backed the Kapp Putsch were not exactly welcomed, they were still able to leverage a connection between the Reichswehr and the KMT. These included industrial companies as well, who, seeking external markets, saw China as one of the remaining countries open to German goods.

After Bauer died, the Great Depression occured, and Sino-German relations took a downward turn, especially as a lack of decisive leadership and conflicting interests between the industrial entities and the military advisors resulted in chaos in the German mission, with some Chinese being offended enough by the Germans that the KMT was seriously considering kicking them out. The leadership arrived in the form of former Chief of Staff and head of the Reichswehr Hans von Seeckt, who brought a great deal of prestige and legitimacy to the German mission. While Bauer had already taken some steps to begin modernizing the KMT's army, von Seeckt was the one that essentially created the model for how the KMT's army should be modernized. He proposed new training regimens, reorganized and centralized military forces directly under the KMT's leader, Chiang Kai-Shek, the creation of a skilled and loyal officer corps, and introduced mobile light infantry tactics. These changes were very similar to those he oversaw in Germany, and to an extent I would consider his idea of creating an elite mobile force to have not been overly considerate of China's massive manpower but limited industrial capability. Still, it was a significant step forward from what basically amounted to pre-WW1 doctrine by Chinese troops.

Around this time was also the rise of the Nazi Party in Germany. Having seized power, the Nazis chose to begin rearming and reindustrializing Germany in preparation for war. Key war materials were desperately needed, and due to poor relations with the Allies and their colonies, many of the resources Germany needed could only be found in the Soviet Union and China. And so Germany worked with both the Soviets and the Chinese, trading industrial knowhow, weaponry, and advisors in exchange for raw resources.

In China, this first took shape by consolidating all German interests in China from private entities into a single "Hapro," an ostenibly independent private company that represented all the German interests together. Subsequent trade agreements were signed whereby the Chinese were able to purchase German weapons and industrial equipment in exchange for raw material. Because of a massive currency problem in the 1930s, caused indirectly by the Great Depression (where a desire for hard currency caused significant outflows of "silver dollars" from China due to speculation), China's government was low on actual cash, and deemed not creditworthy by many financial institutions. This neatly sidestepped the problem of being able to afford the equipment. This also helped with large scale railroad construction through the interior of China, which critically were owned by the Chinese and not a foreign power. Thus when wartime came, Chinese logistics were able to maintained through these large railways, whereas railways owned by the British were barred from Chinese use during the early stages of the Sino-Japanese war.

The structure set up, von Seeckt passed the helm over to Alexander von Falkenhausen, who was probably the most important of the leading figures in Sino-German cooperation. Falkenhausen, like many other German Reichswehr officers, had sought advancement outside the military (which, having a mandated number of officers and personnel, meant promotions were rare). He came up with the details to suit von Seeckt's plan, although he cut corners in preparation for a war that might have started in 1939. Chinese divisions were resized to 10,000 men from 5,000 (characterized as "new-type" divisions), in line with those of Germany. The Chiang Kai-Shek rifle was introduced, a variant of a interwar Mauser design. Hundreds of thousands of Stahlhelm, the German helmet, were issued to Chinese troops. By the time the war started, von Falkenhausen had succeeded in fully modernizing 8 divisions and partially modernizing another 8, still far short of the overall goal of 60 but still able to fight the Japanese in Shanghai for months. Combatwise two of the new Chinese divisions would be on par with one of the Japanese ones, but this was mostly due to the fact that the Japanese divisions were twice as large compared to the Chinese ones. While the unmodernized counterparts were still mostly inferior, they could be modernized and mobilized over time-as indeed what happened throughout the war, albeit at a slower pace than at peacetime.

The German trained divisions were for the most part decimated after the Battle of Shanghai. Falkenhausen urged Chiang to keep his elite troops in reserve and to deploy them at the still-under-construction defense line near Nanjing, but Chiang felt that by fighting near the foreign concessions in Shanghai, they would be able to win sympathy from the Western powers such that they would intervene at the Japanese invasion of China. This move was a tactical mistake (though possibly a logical strategic decision) as in doing so Chiang's best troops were severely attritioned in urban combat. On the other hand, the escalation of the conflict by Chiang forced Japan to invest much heavier into the conflict, thus turning the war into a total war, one Japan simply could not afford. But that's another story.

Sources:

Forgotten Ally, Rana Mitter (the previous book)

Yue Lan, General von Seeckt and Sino-German Cooperation.

Jay Taylor, The Generalissimo: Chiang Kai-Shek and the Struggle for Modern China.