Building　extraction　from　very　high-resolution　remote-sensing　images　still　faces　two　main　issues:　(1)　small　buildings　are　severely　omitted　and　the　extracted　building　shapes　have　a　low　consistency　with　ground　truths.　(2)　supervised　deep-learning　methods　have　poor　performance　in　few-shot　scenarios,　limiting　the　practical　application　of　these　methods.　To　address　the　first　issue,　we　propose　an　asymmetric　Siamese　multitask　network　integrating　adversarial　edge　learning　called　ASMBR-Net　for　building　extraction.　It　contains　an　efficient　asymmetric　Siamese　feature　extractor　comprising　pre-trained　backbones　of　convolutional　neural　networks　and　Transformers　under　pre-training　and　fine-tuning　paradigms.　This　extractor　balances　the　local　and　global　feature　representation　and　reduces　training　costs.　Adversarial　edge-learning　technology　automatically　integrates　edge　constraints　and　strengthens　the　modeling　ability　of　small　and　complex　building-shaped　patterns.　Aiming　to　overcome　the　second　issue,　we　introduce　a　self-training　framework　and　design　an　instance　transfer　strategy　to　generate　reliable　pseudo-samples.　We　examined　the　proposed　method　on　the　WHU　and　Massachusetts　(MA)　datasets　and　a　self-constructed　Dongying　(DY)　dataset,　comparing　it　with　state-of-the-art　methods.　The　experimental　results　show　that　our　method　achieves　the　highest　F1-score　of　96.06%,　86.90%,　and　84.98%　on　the　WHU,　MA,　and　DY　datasets,　respectively.　Ablation　experiments　further　verify　the　effectiveness　of　the　proposed　method.　The　code　is　available　at:　https://github.com/liuxuanguang/ASMBR-Net